By authentic it also means with serial numbers present. Early this century, lots of grey market dealers sold off SMP300's with serial numbers blurred/polished off on the lugs. I believe Omega will not accept and service these; they would have to be serviced by an independent.
I had one of those, fortunately, no issues. I have to suggest that anyone that is clever enough and puts the time and effort into making a decent fake watch would have no difficulty producing fake papers and warranty cards. Come on!
Glad to hear your experience went well with a SMP300 with polished off serial numbers. By no issues; do you mean you had a watch with polished off serial numbers, and it was accepted by Omega for service?