The "Just works" philosophy can sometimes make it extremely frustrating and difficult when it doesn't!
OK, just to be sure we are looking at the same solution(s)...
This is the one that I mentioned:
QUOTE
1) Follow the hints here: <
https://discussions.apple.com/thread/4301699?start=15&tstart=0>
2) If that fails (e.g. if there is no evidence anywhere on your system of the offending app), you have pirated software on your system (whether you installed it or not - no accusation intended) in which someone put their own Apple Store "receipt" file from a valid app into one they didn't pay for to trick the system into thinking it was paid for. The way to track this down:
2a) Launch the Terminal.
2b) Type: "locate _MASReceipt/" (without the quotation marks) and press Return (Enter).
2c) That gives you a list of installed apps that came from, or have been faked to appear to have come from, the Apple Store. Compare this list to the list in the Apple Store application under Purchases.
2d) Make a short list of those which appear in the "locate" list but not the real App Store list; in the App Store application, select Store -> Sign In, login with that, then pick Store -> View My Account, then (after App Store makes you login again for no reason) select View Hidden Purchases, and eliminate any apps that appear here from your short list of suspect apps.
2e) If your suspects list is just one app, trash that and reboot.
2f) Otherwise open (in a text editor) the receipt file in the _MASReceipt folder inside the application bundle (e.g. /Applications/FooBarBazQuux.app/Contents/_MASReceipt/receipt) of each suspect app in turn, and look for text strings, such as an app name, publisher name, user ID, or other telltale content that has something to do with the app you can't update or get rid of and nothing to do with the app in which you found that receipt file. When you find the culprit app, trash it and reboot.
The main problem is that
YOU HAVE TOO MANY APPS! 
That may cause difficulties in following step 2c & d. I just copied the text in Terminal and pasted it into TextEdit. Then I opened the App Store and compared it to that list. I'm going to follow the link above to look at that post in detail, hopefully there will be comments nearby, also.
The key here is to find what does NOT match in the two lists. Apparently, a hacked/pirated app can 'borrow' the _MASReceipt folder and fools Apple's servers into thinking it is an approved app, namely Twitter, in this case.
But the post following the above 'solution' has a different method. Unfortunately, I think it would still require finding the suspect app and it also involves a different Apple ID problem.
QUOTE
I had the problem of App Store Twitter Update from an unknown apple ID. This is how I fixed the issue, hope works for others as well:
1- Start MAC Apple Store.
2- From Menu Bar Select Store then View My Account.
3- In the Account Panel, click "RESET" Reset all warnings for buying and downloading.
4- Click DONE to exit.
5- In the Apple Store search box, type and search for Twitter
6- Select "Twitter" only from the given options and click to install it. A fresh app will dive into your Launch Pad and starts downloading with your own apple ID.
7- The Red Update No. will be removed from App Store icon on Dock.
8- Once app is downloaded and installed, you may uninstall it (like other apps) if you don't wish to keep it.
I've never used this procedure and I don't know what "The red Update No" actually refers to.
If you're ever down near the server farm you might try unplugging the power into the building. They probably never do a cold restart on those computers...
