This problem presents in a number of different ways. I had the same problem with updates to iPhoto, Keynote, etc. on my 2014 MacBook Pro However when I clicked on the purchases tab of the App Store application, all I saw were listings for OS X Yosemite and OS X Mountain Lion with a download button on the right. Strange, since the Yosemite update completed and could be verified using "About This Mac" (and clearly the Mountain Lion upgrade was ancient history). There was no listing of the problematic apps as describe by others and therefore no ability to accept them.
However, I eventually noticed that it was possible to update these apps through the updates tab. You don't click on the "Update" button. Instead you'll find that clicking on the app name opens up a description of the app and then you have the ability to update it on that page. Did this for iMovie and iPhoto and all suddenly worked fine with no Apple ID problems. Strangely enough, when I then looked at the purchases tab these apps were listed and I could follow the procedure outlined by others for Keynote, Pages, etc.
So, don't get discouraged when you find your situation differs from what others have experienced. Keep exploring and you'll hopefully find a way to accept each update individually. The only application that hasn't worked for me is the update to Aperture. The Apple ID field remains incorrect and greyed out regardless of my approach. Thus I can't provide the correct Apple ID and password to make Aperture compatible with Yosemite.
Lastly, the strange part of this is that during the update to Yosemite, I was at some point asked for my Apple ID password. The Apple ID field was automatically populated, but it was partially incorrect. It was listed as "appredeemer@xxxxx.xxx", with the correct domain (xxxxx.xxx) from my true Apple ID password. Seemed like a funny hybrid of my Apple ID email domain with a generic identifier. I corrected it and the installation completed with no problems. I wouldn't have thought much of it, except for the fact that all of this "Update Unavailable with This Apple ID" b/s is accompanied with Yosemite autofilling the greyed out Apple ID field with "appredeemer@xxxxx.xxx", the same bad Apple ID that popped up during the install. Really makes me wonder what's going on.