I was given 12+ hours notice that my 1st leg on DL was canceled this morning (mechanical). I need to be home tonight, so I asked to be rebooked on a UA flight which had plenty of availability. DL agent called UA and got me booked with a confirmation number and confirmed seats.

I show up at the airport at UA tells me that they aren't accepting any Delta passengers because they're oversold. I politely remind the agent I was confirmed some 7 hours ago; he curtly continues to repeat that they won't accept me. I ask to speak to a supervisor; he disappears and comes back, saying I need to go to the DL counter and get a ticket number.

I oblige, return, and he proceeds to issue me boarding passes. However, he tells me they may have to deny me boarding because they're still oversold and "I'm not yet a UA passenger, I'm still DL's problem.". I say I have a ticket and a confirmed seat assignment... He continues his stance, even going as far as saying that if they deny me boarding, it's delta's issue concerning compensation.

I'm pretty sure I'm 100% UA's responsibility here. Am I right?