So I checked my TIme Machine back up, and no, the app is not there. Thanks for the hint.
The App is Twitter, which is a free app. I tried to download it with my ID, and when I try, this is what happens:
Find Twittre in the Mac App Store.
Click on the "Free" button
Click on the Install App button
Sign in sheet opens with my friend's Apple ID filled in.
I change the Apple ID to my own, enter my password and hit Sign In.
I then get: There was an error in the App Store. Please try again later (4).
Then a second sheet: Unknown Error
I am able to download other apps.
Any idea how to tell the Path the MAS thinks the app is in?
This solution for finding pirated MAS apps may also help you hunt down what is being seen by the MAS;
Finding a pirated app
All MAS apps have a MAS receipt in their app bundle. Check any app acquired from the MAS. Right click on the app's icon in your Apps folder and choose Show package contents. In the Contents folder is a _MASReceipt folder and in that folder is the coded MAS receipt. It has the Apple ID of the MAS account that bought/acquired the app from the MAS. It is that receipt that the MAS uses to alert you that an app has an update. There would not be a notice of an update with someone else's Apple ID showing in the MAS on your Mac, if there was not an app with a receipt from this person's account somewhere on your Mac.
Download the free app FindAnyFile (FAF);
This app is easier to use and seems to be more powerful than Spotlight. Open FAF and in the box type _MASReceipt and press Find. It should come up with a list of every app on the Mac with a MAS receipt. Compare the apps with receipts in FAF's list with your purchased apps list in the Mac App Store. The odd app out should be the pirated app.
I wouldn't exactly called the free Twitter app Pirated if I copied from another person. The app is free.
I used both locate on CLI and FindAnyFile and was able to locate all my AppStore apps, but not twitter.
I then used fs_usage and monitored the App Store process, which led me to come plist and cache files, which I deleted but no luck, twitter was still there.
I did not say that the app was pirated. I said that this process for finding pirated apps might also help you with your problem.
However, now that you have brought it up, whether the app is free or not, the Apple End User License Agreement for apps acquired through the MAS does not authorize anyone to copy an app acquired with someone else's Apple ID. It is pirating.