The wikipedia answer is that they want published sources that people can cite and review.
This seems a bit crazy when the famous person is someone you respect and trust, but as soon as self-publicists, frauds and quacks get involved, this becomes a useful guideline. And of course you can't have one rule for some and another rule for the rest.
Bingo. Just because the person in question may even be the topic of the article, it doesn't mean that person can't be biased or want to spin things a certain way. By requiring citations and sources, you're providing some validity and "proof". Granted, sources can be faked too, but the level of separation works to minimize much of that. The faking of sources isn't something that would be very common anyways.
It sort of falls back on the Perfect Solution fallacy. You can never have a perfect solution so you have to choose the "least bad" option. The option with the least drawbacks or negatives.
We can (and do) have recognition only for some (and not just for everybody, i.e. "the rest"). It may be a flawed solution, but that is how things work in the real life.