It doesn't really go on disability as such, they look at what needs you have that other students don't. So for the person with aspergers, if it's bad enough that they really can't share a bathroom they may get en-suite cheaper - because they're having extra costs as a result of their disability. But that doesn't mean everyone with aspergers is automatically entitled.
And no, it's not easy to exaggerate because they need evidence, like medical notes.
If your SB means you find climbing stairs harder you may be given groundfloor accommodation, or somewhere with a lift, or things like that. If you find carrying things is difficult then you might get more photocopying allowance, so you can photocopy bits out of textbooks rather than having to carry big heavy books home.
But you won't just get cheaper accommodation if there's no reason for it.