Option to "prove" the giveaway is legit using the Steam public inventory

Users creating fake giveaways get banned soon :) not needed

Honestly, I don't see how there is a problem. There is a system in place that prevents people from making dozens of fake giveaways and points add up pretty quickly.

Besides, I see so little on this site that I am actually interested in I would rather use my points to make a bunch of invites and get new people on the site, so it may lead to more neat stuff being posted.

The biggest problem is that very few users have their inventory viewable by the public. It's hidden by default, so a user has to explicitly change the settings in order for it to be viewable.
Few people ever change their Steam privacy settings, and many of those who do prefer to keep their inventory private.

So any flag denoting that the game is in the users inventory depends on the inventory being publically accessible, which it seldom is so such an addition while beneficial in theory would very seldom ever show up.

Most fake giveaways are for the big AAA titles (to get points, I assume). Why not add points after the giveaway ends and the game given/received.

Some of the big gifters hide their inventories because people constantly look.

I don't think it's really necessary.
Want to prove your giveaway is legit? Take a screenshot of your inventory and put it on the giveaway description.
Done.

How DOES photoshop work?
:D

Hey, criticsquid. Anything that requires SteamGifts to force members to keep their inventory or profiles public will not be an option. When a giveaway is flagged, we'll ask a user to present evidence in some form, but it's entirely up to them how they want to handle it.