How to get Mac App Store to stop thinking app is installed on external drive?
Figures I found someone else that runs into the same problem as myself and no one has answered with a solution yet.

What I can offer is a work around for now until someone chimes in with a better fix, because I have an external drive that I use as backup by cloning my OS X partition. So when I decide to format and reinstall fresh I run into the same problem as you except I can't even install the apps because it says they're already installed.

Simple and Quick - Just disconnect the drive and restart the App Store, it will refresh with the correct information.

-Idea's I've been kicking around, but have not given it much more thought or a go.

I was going to make the drive hidden by putting a "." as the first character of the partition name, but I kept running into another problem (can't remember).

Anyways I hope this will work for you since anytime I've ever ran into the issue i've always resolved it by disconnecting the drive. 

Good Luck!
-Mac