My DD uses a wheelchair and can't walk or stand, so there would have been no way to accurately measure her size. It's not obvious that she can't stand just from looking at her. At various times, she has been on everything except Space Mountain, Rock N Roller Coaster, and Big Thunder Mountain.
She's now over 60 inches tall, so size is not an issue. When she was younger and smaller, we were sometimes asked if she met the height requirement, but no one ever asked if she was able to get out and be measured. It was our responsibility to make sure that she was OK for any restrictions for that ride.
Some people (like my DD) are not able to get out of the wheelchair or are only able to stand with difficulty. From our experience, they don't make a big deal of measuring those people, as long as the parents know the child's height and verify that they are tall enough. I don't think that getting measured for some rides where the child is kind of "iffy" is unreasonable to ask for someone who is easily able to get out of the wheelchair and stand for a few minutes for measuring. (I do understand that some kids who can physically do it easily, might not be able to do it easily for behavioral reasons).
If you are going to the doctor before your trip to WDW, you might want to get something official looking from the doctor that states the child's height. I don't think you would need it, but it might be useful (I definately would not make a special trip to the doctor to get measured, but if you don't have a visit scheduled, you may be able to have the nurse send you something indicating the last measurement).
