The first thing to mention is that when you open Steam website and open some free game you "own" and actually shows that it is in your Game Library. So, it is unlikely that F2P games are counted as "owned" only when you have them installed.
Also, recently I was forced into deleting everything from my Steam folder except
userdata folders and
Steam.exe itself. Still, all my free-to-play games was there, even the ones I've never installed and played. So, I can assume, that if @kotekzot is right then the files mentioning all this F2P games should be in this two folders.
I've conducted a search through them using Magicka: Wizard Wars with an ID 202090 as an example. Actually, I've found nothing related to this game, not a single file, neither in
steamapps folder nor in
userdata. Still, as I mentioned, game is present on my account, so I have totally no idea where could lie the file that mentions this game.
So, summarizing all this I think this issue can't be resolved without further research.