I've had mixed experiences on this with different clients. It's very bank specific, and even the same bank will often change its KYC policies.I'll add one additional factoid to this. According to my BA bank's policies the USD -> USD transfer is OK so long as it is "family" money - you are sending to a parent's account, son's account, etc. Or it can be your own account as mentioned.
I mean, the worst case scenario is your money floats around for a few days or weeks and then gets sent back (minus fees, of course, because banks will make money of you even when they mess up).
For these amounts I would go to the trouble of writing up a simple document and getting it notarized and, optionally, apostilled (this last part might not be necessary depending on the bank).
Easiest is always transferring to your own account or spouse to spouse, but even if you do that I would still have some sort of document drafted because banks will still want to know why you're moving the money and also it'll help in the case of an (unlikely) tax audit.
Edit: also, @rdino I would avoid a wire transfer initiated by your friend. If it gets reviewed it's going to be extremely hard to get the bank to approve it.