Ability statements are somewhat related to the tradition of the self-narrating zoo exhibit, and I'll explain why. First of all, I think people tend to get told their disability is mild (or something else, but whatever the words are they usually imply it's not a real disability) when they haven't gone into a lot of detail about their disability and how it affects them.
The thing is though that there's no correlation between how much you talk about your disability and whether your disability is real or not. So why do people imagine there is? I think it has to do with the expectation that disabled people who talk about disability will always be talking about their own disability. A writer who self-identifies as disabled, but isn't describing her own disability, produces writing that is inconsistent with what's expected from a disabled writer. Maybe this is why the legitimacy of her disabledness gets called into question.
I think some people who have made ability statements would argue that they weren't telling the disabled person her disability wasn't "real." They were just arguing that as a talking person, the disabled person doesn't understand the experience of people who can't talk (or whatever the ability in question is). But in the context in which ability statements appear, they almost always are jarring in the extent to which they don't follow naturally from the conversation.
"I am disabled, and I think--"
"You can talk."
"I know I can talk, but anyway I'm disabled, and I think--"
"You're less disabled than someone else."
"I know I'm less disabled than someone else, but I was just saying--"
"You can attend college."
"Actually I had to drop out of college for reasons related to my disability, but anyway, I had something to say, and this is kind of offensive."
"Why are you denying that there's a difference between you and people with severe disabilities?"
As a queer person, I can make this comparison, I think: someone who's talking about something "as a queer person" doesn't usually have a lot of straight people clamoring to tell him that he's bisexual rather than gay, or that he's "straight-acting," or that he came out late in life.
Queer is a pretty broad word and so is disabled. If someone is talking about disability as a broader category than some really specific thing like not being able to talk at all, then I don't really see the motivation for needing to pin down a lot of specific facts and--it often seems--put the disabled person in her place by highlighting ways in which she is "less disabled" than someone else.
I don't think it is surprising how much it happens, because the way disabled people are treated is often all about putting them in their place for wielding the term "disability" themselves instead of letting someone else have it (and that has to do with the next thing I'm going to say). But when it happens it is really offensive because it takes a conversation that was often more abstract or general and steers it into being about the details of the disabled person's life.
Ability statements are a personal attack because they are dehumanizing. By throwing them out there when they are irrelevant, you indicate that a disabled person doesn't have the right to just express ideas and feelings like you do. She must be on display.