Although the standard for disability is to be able to support oneself- I have to agree: if you are working and making any income through that, even part time to any degree, you are very very likely to be denied. It's actually pretty much a given.

There are a lot of things that are more complicated, that involve a lot of individual factors, but that has been pretty consistent from what I have seen.

You can work while on disability, after being approved.
Starting after the first couple years I've had various part time jobs in an effort to regain sellf support [and not been terribly successful, but that's a different story]. There is a limit to the income and there's some complicated restrictions eventually, but it doesn't automatically effect your benefits or anything.

During the application process, it doesn't look great to the SSA though.