If the suggested accommodation does not work then Disney is required to find one that works as long as it is not an unreasonable burden.
It is funny that the change in the nature of the event is not a protection for the company but was always intended as a protection for other attendees so that there experience was not significantly changed (degraded) because of the accommodation, in this case since it is about the access, not the event it would not apply.
Safety is always first but there are lots of ways that Disney could safely accommodate this situation (and no Disney having to issues a photo "height pass" would not be considered an unreasonable financial burden to Disney)
4disneyNUTS
The standard for schools is somewhat different under IDEA, the rulings there are that an accommodation can not be denied because by "administrative convenience" (and that needs for FAPE must be met).
bookwormde
People have posted quite a few times in the past that they did ask and were told this was not an accommodation Disney could/would give.
I would like to see some documentation that shows a recreational facility/amusement park would be forced to go to that level of accommodation. (there are different guidelines/requirements for work and school settings).
If an accommodation would cost much and benefit few, it does not need to be made. I think this would fit into that 'bin'.
There are relatively few people who have problems with being measured because of reasons like the OP mentioned.
Sure, it might be relatively inexpensive to add photos to GAC ( and that might be a good idea anyway). And, it might be fairly inexpensive come up with a procedure and to train the Cast Members in Guest Relations to do hje measurement and put them on the GAC.
But, a child who may not stand to get their measurement done at attractions also may not cooperate to get it done in Guest Relations either.
And, another huge and expensive part would be training each and every employee who may work at an attraction that has a height requirement. This would be a huge undertaking and I don't think (IMHO) would be reasonable given the small number of people who would potentially benefit.
Besides that, there is the safety angle. Any workarounds or policies that are changes from how a safety procedure is normally done are potential break points where safety can be compromised. You want as few breaks as possible and I can see that having the height on the GAC would be a huge break point. IMHO, an accommodation that requires a change in the safety procedure is seldom reasonable.
For example, Peter Pan has a moving walkway. I could argue that stopping it so we can carry DD on is a reasonable accommodation and should be required because we can't go on without stopping the moving walkway to get on and off. And, they do it for other attractions, including Haunted Mansion, very close by. We need the moving walkways stopped for physical reasons ( we are lifting DD on), but some people are needing it for more psychological reasons (their child won't step onto a moving walkway.) for those attractions where it is safe, Disney does slow or stop it. For a number of reasons, including the fact that riding guests are suspended above the ground in hanging pirate ships with no positive restraints, WDW has concluded that stopping the moving walkway to let people with disabilities board is too much of a safety risk. So we can't ride.
Lastly, a lot of people have posted about concerns regarding their child being measured. People have pretty consistently recommended practice and/or social stories and the OPs have posted back that those things worked and they were very surprised that their child did very well with measuring. I don't remember anyone ever posting back that they had prepared, but still had issues at the park related to being measured.
It's too bad you can't have your kid measured once at Guest Relations....
I wonder if Disney has had this request before. 
