I have turned down sales that were explained to me as "gifts", and I have allowed them. After time, you get a good feel who is being truthful with you and who is trying to circumvent the law.
Years ago I was refused a sale of a shotgun, when the guy behind the counter heard me tell the friend I was with, that my brother is really going to happy this Christmas. Guy behind counter says "this is for your brother?", I said yes for Christmas gift. The guy took the shotgun off the counter and said I can't sell it to you because it would be a 'straw purchase'. Argument insued, his store, his gun, he won the argument. The gun store was Southwest Shooters, they went out business, I bought the gun somewhere else and kept quite about my intentions.
Here's my understanding of the issue. In the state of Oklahoma the act of buying a gun for someone else (such as in a gift situation) isn't ITSELF an illegal action. Lying on a 4473 and providing a firearm to someone restricted from owning one are both crimes. If buying a gun for someone else involves either of those two things then it is a crime. Since private party transactions don't involve a 4473, as long as no one involved is prohibited from owning (felons, etc) I don't think it would be illegal in Oklahoma between Oklahoma residents. Does anyone with any real (vs what I'm pulling out of my a$$) legal knowledge know?