Waaay back when, I believe it was expected of the GA creator to do his due diligence and check the winner's library ahead of time, that's the only reason I ask really. I couldn't find it in the guidelines explicitly though when I searched just now. That said, the rules do state the following:
Does my Steam profile need to be public to use the site?
........However, if you wish to enter giveaways, the site will ask you to switch to a public Steam profile once a week to bring your account up-to-date.

So to address your second point, you being able to enter the GA only tells me that you haven't owned the game for more than a week. I totally understand the want for a private profile though (mine would be if it wasn't for the above rule) and I've added you on steam for the verification.

Thanks for your understanding :)