Way to check Private Profiles for verified wins

yes, request a reroll from the giveaway winner page. support can check and they will let you know if the reroll valid or not.

Could always send them a friend request to check that way.

Edit: Or as Mully says could work.

It happened a couple times to me, so I wrote in one of their giveaways asking them to either temporarily set their profile to public, or send me a friend request and set it at least to friends-only., in order to verify that they didn't own the given game. One accepted, the other declined and allowed me to ask for a re-roll. Sending a ticket works as well, but I would avoid bothering support for something so simple.

If they don't reply to you on SG or Steam, do as Mully suggested.

Make a request new winner ticket.

Other

and something like:

Winner has a private Steam profile.

Can you please check and advise?

If they deny = no re-roll

if they approve = re-roll