Although I think the problem likely rests with UA, there is the possibility that DL created the ticket for you with UA but UA never actually ticketed it or DL never re-ticketed it.

If the reservation was actually ticketed then this is 100% UA's fault and they have no grounds to deny you. If the reservation was not ticketed then it's either DL's fault for not forcing the reissue or UA's fault for not doing it.

It sounds like you made it on your flight so in the end this all worked out OK. Do you remember what the ticket number started with that you got from DL and brought over to UA? If it started with 006 that means it was still ticketed by DL and would be DL issue.

-RM