I believe what the Legislature had in mind when they used the word "access" was simply the ability to get to and from a residential property by conventional motor vehicle.   

In my experience, most private roads do not have access to city amenities such as sewer and water.  Access to power, phone lines, or cable service is granted by the owners of the property which it crosses.

To illustrate what I believe the Legislature was trying to protect, I'm attaching two photos.  The first (taken years before section 3121 existed) is of a road that had no maintenance agreement in place (and on which most of the landowners were woodlot owners, who under section 3121 would have no obligation to contribute to maintenance.)  Lenders want to know that if they are financing a home, the homeowner will actually be able to get to and from that home, and their ability to continue to do so requires that there is some mechanism in place for keeping the road passable.

The second photo illustrates why section 3121 is intended to apply to private roads only, not to former town or county ways that have been abandoned or discontinued.  Unfortunately, use of the term "private road" without providing any definition for that term has led some sellers to believe it applies to any road that is not maintained by the public, therefore including discontinued roads.  On such roads, there is the danger that another landowner may acquire property on both sides of the road and then claim ownership of the full width of the road, denying ALL access.  That is what happened here, after two buyers had been assured the road was a "private road with maintenance shared by the abutters."

In short, if a person uses a private road to access their home by motor vehicle, they should share in the cost of maintenance.

Ah, sorry I misunderstood the root of the problem you were asking about.  I think you are trying to apply the wrong statute.  Section 3121 was put in place for the primary purpose of assuring lenders that a residential property they are financing will remain accessible (i.e. not become functionally land locked due to lack of maintenance.)

Your question has more to do with someone who has other access, but who may occasionally use the private road as additional access.  You said, "if there is no road association, it is all we have."  I don't believe section 3121 will help you much in this situation. It starts off with, "If more than one property shares a common benefit from a private road..."    I think the resident you are referring to would argue that a person whose primary access is via a different road does not share a common benefit, since, as you say, they do not routinely use the road to drive to their house. 

But if you have no road association, it may well be in your interest to look into forming a statutory road association under 23 MRS sections 3101-3104.  Section 3101 says it includes "the owners of all the parcels benefited by the private road."  

It does say, "When 4 or more parcels of land are benefited by a private road, private way or bridge as an easement or by fee ownership of the private road, private way or bridge..."  But I think that has more to do with establishing the existence of the road as a private road, than dictating who will be members of the association.  It then goes on to say that notice of the initial meeting must be sent "to the owners of all the parcels benefited by the private road, private way or bridge ..."  I would argue that a statutory road association therefore includes everyone who benefits from the road, regardless of whether it is their primary access to their residence, and regardless of whether they have any easement or fee ownership of the road.  In the case you describe, it certainly sounds like this property is "benefited by" the road.

There have been disputes before over whether a person must pay dues to an association if their property abuts the private road but they do not use that road for access to their property.  The usual conclusion is that while the association may decide it's "fair and equitable" to charge them at a lower rate, they do need to pay something because the road does provide access to their property, which they could decide to use at any time.  It also provides emergency access in case, for example, there is a brush fire on the back side of their property.

If you were to form a statutory road association, you would then be able to use the "Notice of Claim" process if necessary to collect a fair assessment for this person's use of the road.  You might, however, decide that "fair and equitable" would required charging them a lesser assessment than those who use the road daily as their primary access.

One final thought - if I understand you correctly, you were hoping to use section 3121 because you have no road association.  Section 3121 essentially creates a road association, but aside from a passing mention of "after reasonable due process and notice,"  it gives no guidelines for how that is to be done, and the only enforcement power is through taking the offender to court.  So the only reason I can see for trying to use section 3121 instead of 3101 in a situation like yours would be if you do not have section 3101's required four landowners, three of whom agree to call the initial meeting.  If you are having difficulty getting those three original signers, I would strongly recommend you attend the MARA Conference on Oct 4th, where you can network with others to learn how they got started.

I think the second passage you cite from section 3121 hits the nail on the head as far as why 3121 does not apply in your situation.  As I said before, the statute was designed to make sure a residence would not be denied access due to physical deterioration of the road.  In your case, the private road could become completely impassable, but this resident would still have access to their home over the public road.

You are trying to wring some meaning out of the statute that would make it apply, while she can look at the statute and argue why it does not apply.   I think there are better tactics for your suggestion of getting the owner to reconsider her position.   

You might try first asking why she feels it necessary to use the private road at all, since she has better access over the public road.  And don't ask in an accusatory way, but ask as if you are sincerely interested in hearing her thoughts.  Then ask what effect her uses may have on the road.  She may have had no choice as to the route utilities take to get to her house, but if those utilities need services, the contractors' heavy trucks and equipment that come to provide those services will need to use the private road, and will cause wear and tear on the road.  Having guests park on the private road is a convenience.  If you can get her to realize that she is gaining valuable benefits by her use of the private road, and if you then point out that her use of the road does contribute to wear and tear on the road, maybe she will see why you think she should pay dues.  (But she may be justified in thinking she should pay less than those whose daily trips over the road cause more wear.)

We had good results from telling the first person on our road that if they wanted to move their driveway around the corner onto the public road and block off all entry from the private road, we would not charge them dues.  We also pointed out that the amount we were charging was comparable to the cost of plowing a driveway.  They decided to keep their driveway where it was, and they have paid their dues without complaint ever since.  So you might try suggesting to her that if she moves her utility entrances around onto the public road, has her guests park on the public road, and blocks off all access to her home from the private road, you will not charge her dues.