Um so, first of all you posted a different speech that the one we are discussing. The one that is current was posted here:
Biden's fact check record isn't great. He's made more false/mostly false statements than he has true/mostly true ones. and most of them are optimistic oversights....he isn't lying to protect a fucked up agenda like republicans, he isn't lying at all...he has an optimistic outlook, and speaks...
www.rollitup.org
Secondly I did listen to what you posted, and he didn't refer to politics at all, again you inserted it. What he said in that video was "I got started out of an HBCU, Delaware State".
The audience likely didn't know where he went to school, and assumed that he knew himself where he went to school. It does really seem like he has Delaware State mixed up with his school, Delaware University. Is it a big deal? Not really, but I do think denialism of the statement is kind of a big deal.