Pistoff I had to re-read that a couple times because my first reaction was the same as yours. But it looks more like they referring rooms for those who are financially needy, not people who are handicapped.
It does seem a bit ambiguous, maybe they are trying to say no handicapped people without actually saying it. If that were the case I would imagine they could be in some sort of legal trouble or at least get some nasty press from the ACLU.
They obviously made some sort of deal with the hotels if they have to stay in an aproved hotel for the whole 6 days.