How can a connection for one DB block a connection to another DB in SQL Server?
So there's a couple of ways that this can happen.


The queries in the blocking database reference objects within the blocked database.
The queries are waiting for tempdb to allocate pages and one query is blocking another query.
There is memory pressure and queries are waiting for memory to be allocated so they have to wait their turn in the memory allocator.


If you download and put sp_whoisactive on the server it'll give you a lot more information about why things are blocking if this happens again.

Given your note about the memory pressure you probably were suffering from either #2 or #3 on my list above.  Odds are it was memory not being able to be allocated fast enough, but it's possible that because you didn't have enough memory stuff was spilling to tempdb faster than tempdb to do "stuff".