Rarely would I accuse a Delta agent of telling me a "lie," but there are too many times when out of ignorance (largely because Delta's complicated rules change every two weeks), a Delta agent will "misinform" me. I think this was a case where a customer was misinformed.

Having said that, it was printed out on that itinerary, and NOBODY gets a hard copy ticket anymore, much less the fare rules associated with that ticket, so IMO the OP has a valid complaint.

What I would probably have done in that situation is not fork over the $270 at that time, but instead go back to the Delta counter and check the bags on the original (delayed) Delta flight. The bags arriving 6 hours late sound like a manageable problem as opposed to the unattended pet with the full bladder.