It would be useful to know which state you are in. There could be differences.
In the ACT, where villa/townhouses are generally what is termed ‘class B’ units, it is unequivocal that if the driveway is shown as part of the lot, then the owner is responsible to maintain it entirely, not just the surface.
Elsewhere, I would be surprised if a similar view did not prevail. I suspect your owner is just ‘trying it on’.