The problem Peter identified above -- PSA verifying/authenticating cards graded/authenticated by its competitors (SGC BGS etc) -- is a significant. I think its an invitation for mischief. Why would PSA want to make their competitors look anything but bad...,.I just (today) sold an obscure Cuban issue (a booklet page) that SGC graded (authentic) that PSA would probably not grade. I haven't seen any graded by PSA and the item in question may not meet a common definition of "card."
https://www.ebay.com/itm/204455457982
So I'm shipping it to PSA to authenticate (or whatever). I actually did not know about this until it happened ... I wasn't up on how the guarantee worked with respect to non-PSA cards -- I don't sell much anymore and recently I've only sold PSA cards .
So judging from what I just read above this could be a mess. I wonder how PSA would treat (for example) a Football Exhibit card from 1948-50 when PSA doesn't grade them but SGC does. Or maybe some Star basketball card from the 1980s that BGS graded that PSA has not yet decided to grade.