I have never had a problem replacing parts through AZ. I have replaced my brake pads/starter/alt. on my Samurai 3 or 4 times each and they have always been happy to do it. I have Duralast alt. on my SD with no problems. I agree that some of their parts are not as good as say NAPA or motorcraft but if you can replace it yourself (something simple like a alt. change) I would do it.
About exchanging it under another persons name, they never check ID. Hi, I'm John Doe, here is my phone number. No questions, as long as you know the name/phone number.
On another note, my local NAPA dealer exchanged my battery, no receipt or date of purchase and I told them that the dealer bought the battery and not me when I bought a used Town & Country. The prorated it from the month I bought the van. No questions, no problems. I was impressed with that.