This has never happened to us at Disney related theme parks. But it has happened at Busch Gardens in Williamsburg.
In the mid-90's my husband had a broken ankle. We already had a family outing planned for the day, so we felt obligated to go. I pushed him around the hilly park in a wheel chair (because we were too cheap to get the electric one).
Every ride we attempted, he would start to get out of his wheelchair to wait in line and a staff person would rush over, and show us the handicapped entrance where I could push him almost right up to the ride. He'd get out, waddle over to the ride, get in and we'd be off. Each ride, they'd offer to let us go through a second time. Plus, we were with 2-5 other family members (depending on the ride) and they got to go through with us, too.
It was in the heat of August. The people in line where really, really mad at us. And we could hear them literally cussing us out as our roller coaster trains left stations.
The thing is, we didn't ask for this special treatment. They offered it to us. On a hot summer day, with lines 60-90 minutes long, it really made up for me having to push him all over the park.
