To dispel the rumours.
There is NO EXP challenge. None. Nada. Never.
And I mean this in the sense that you cannot call AA and ask for it. And Aadvantage will deny it till the cows come home. Because there is no Exp challenge. There isn't.
However -
Just as many business's have, there are internal "committee's" for want of a better word, that do want the 1k's from UA and do want the big flyers from other airlines. No surprise there. It's their job to get that person from UA to AA and make money doing it. And in the scope of their duties, it's within their power to offer whatever it takes to prove you are putting your butt in AA's seat and continue to keep that butt there for years to come
If the word challenge has been termed by the OP, that's what the OP decided to call it.
Suffice it to say that you must, more or less, be targeted for something like this and no amount of begging, pleading or threating AA is going to get you anywhere. Your name is not going on some special list, your account isn't going to be audited for past activity and your best bet is to show some high end love to AA, build a base and send your inquiry to Customer Relations or ACS where it will be forwarded to the right people who may be able to offer you, something.
Being smart elite flyers, I'm sure most potential Exp's know how to plead their case to their potential new airline. But you can bet, being just a plain old 1k isn't gonna do it. There's a bit more to it.