I've had more than one DB open at the same time from the same terminal, both DBs being local. I've had one local and one remote DB open at the same time, too.
If you had the means (and the patience; harder to find sometimes...), you would note that in your Access app, you might have more than one member of the Workspaces collection. Each such member represents one instance of Access having been opened.
Where you really run into trouble with this is MEMORY - because Access has so many data structures to build within itself to remember where everything is... and if you have limited swap space and limited physical memory (and therefore, also limited VIRTUAL memory, far more important), you might not get multiple instances up an' runnin'
If you open multiple instances of the SAME DB - you also run into a locking problem because, despite being the same user, you are running two different instances. Unless you handle the locks exactly right, you will get locking violations against yourself! (Heck, don't even need two instances of Access open to do that ... it also happens if you have a bound form with VBA code acting on the recordset of the form and forget to clone the recordset...)