I realize that ArcGIS is 32 bit besides background processing as I wrote earlier.
Forgetting ArcGIS and accessing a .mdb, created with Access 2010 (32 bit) gives the same message asking for a specific driver (64 bit). This led me to believe that 64 bit Access was needed, along with that specific driver so I installed them both.
I have always good luck with the support teams from all vendors. I just need to get everyone together on a conference call when I have more time.
Thanks for all the comments.
The Avenza support answer above was correct, but in a round about sort of way, I guess.
MAPublisher is awesome, that is all I know. However, when it originally installed, it installed on my 64 bit version but not the 32 bit version of Illustrator. I thought since my license precluded me from having more than one instance of MAPublisher running, that was just the way it was so I have never worried about it.
However, my old version of Illustrator (CS5 - 32 bit only) still resides on my machine because I purchased it and I own it and all that. Anyway, when I installed MAPublisher it attached itself to that particular version of Illustrator (CS5) rather than the CS6. I have never used CS5 since the CS6 install so I didn't even realize MP was attached to it.
Everything functions together fine, like I knew it should have been, except for that initial install thing - and the 64 bit version of Illustrator still not seeing the 64 bit driver that is installed. The Illustrator/MAPublisher version I was using was the 64 bit version, and it was asking for that driver. I tried the 32 bit Illustrator, but MAPublisher was not attached to it, so I didn't think too much about it before realizing that the CS5 is 32 bit. I open it and, voila.
Next up, connecting to a File Geodatabase. For now I'm just pleased that I can at least import a .mdb even though not with the Illustrator that I was expecting to be using, although I know it really doesn't matter too much anyway.
Thanks again for the comments.