So, I'm really mixed about this thread.
On one hand, thick soled shoes can make the difference for a child (not for the OP), and Disney doesn not make kids take off shoes, so it is not the child's natural height, but the child's adjusted hieight anyway. What difference does it make if the height is adjusted by the thickness of the shoes, or some inserts, or whatever. Shoot, even the time of day could make a difference (go early, when the child can stand stright and isn't tired

).
However, I'm with some of the others about the message that this sends to the kids. Stuffing something in the shoes definitely sends the message that you are doing something to get around the rules. With an older child, you might be able to have an effective conversation about the purpose behind the rules, but not (likely) with a 4yo.
I don't believe it is a defacto age thing. Many rides DO have an age restriction for riders riding alone (or even for infants riding with an adult). And there are tall young children, so it would be setting the 'age' at a very low level for most of those rides (and, as another poster pointed out, restriciting some adults).
The one thing with this that I would say (and the OP seems like she would follow this) is DON'T try to convince the CM. If the CM indicates that the child is not tall enough, whether at the beginning of the ride queue or right before getting on (because they WILL remeasure on many rides), go along without a fuss. And be prepared for this (what, if anything, are you going to do if the child is not tall enough). Whether you think it is safe or not, the CM is just doing her/his job as instructed, and is not allowed to make a safety judgement call.