Those rights would have had to be acquired by or transferred to Make America Awesome PAC for them to do the ad, or there may be a copyright violation by MAA.
There is a chance he was holding those rights so the image did not disappear down the memory hole, too.
I linked to an eBay page where the GQ issue with that photo shoot was for sale the morning the story broke, (about 180 USD, plus another 20 for 'shipping'). By 6 hours later, the eBay page was gone, as in 'does not exist' gone. Someone was tidying up.