Re: the recipient forwards a copy of his email to a GMail box
I once had a customer who set that up on the mail server that I supplied them with. Their reasoning was they were concerned about the reliability of my on-prem solution. What happened was that a few spams got forwarded to gmail and, as a consequence gmail blocked my customer's IP. Which meant they were unable to send to gmail accounts. "See, I was right to be suspicious about your tin-pot email system" was their reaction.
(Try going through the hoops to unblocdk an IP from gmail's blacklist: it was easier just to use a different one from my customer's IP pool, and to black-hole that user's forwarding abilities so that it wouldn't happen again).