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.