I purchased my iMac using the same (and only) Apple ID I use to purchase apps. Third-party apps update fine, but the apps that came with my iMac (iPhoto, iMovie, etc) bring up a message saying I have to log in with the account I used to purchase them.

I used my only Apple ID to purchase my iMac (Intel-based one).  I've never been able to update core apps that came with it.  I can update third party apps I've bought (like Coda), but when I try to update Garage Band, iPhoto, iMovie and so on, a popup message appears saying "You have updates available for other accounts" and "Log in with the account you used to purchase this app in order to update it", or similar (see screenshot above).
The OS seems to get its updates fine - it's just the core apps from the App Store.
I've only ever had one Apple ID, so I have no idea what to do.  I went to ask the Genius bar at my local Apple store, and they couldn't help, and insisted that I must have purchased the iMac using a different account, but I definitely didn't.  There are a few posts on non-Apple forums of this happening to other people, so it must be a rare bug.
I'm a little concerned it may affect my ability to update from Lion to Mountian Lion.  Can anyone help?
Dan

Have you done a Disk Repair and a Disk Permissions Repair?
If that doesn't resolve the problem I would suggest calling customer support about this issue as it is most likely on their (Apple's) end that the problem exists. 

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