It's a common sentiment among wheelchair users that the freedom they enable makes them feel like an extension of a person. In that context, for the purpose of the "vehicle" question, there's not much difference between a wheelchair, prosthetic leg, or eyeglasses.

I wouldn't say I'm entirely convinced, but it's at least convincing enough that I said that a wheelchair did not violate the "vehicle" rule. I can't define "vehicle" in a way that would satisfactorily justify that decision, but I'm comfortable with that.

The Merriam-Webster definition tends towards a vehicle being something with a power source (something where the power source is not manual/manus/human) capable of moving other things. That would include any sort of powered chair, but not be a problem for a standard wheelchair. Interestingly the Oxford American dictionary explicitly includes a cart as a primary example however, and Wikipedia’s primary example of a vehicle is a bike.