The key to buying a gun as a gift is to never tell the dealer that it is going to be a gift, no matter how tempting it might be to tell the world you're buying a gift. It is perfectly legal as long as it is a legitimate gift for someone who is otherwise allowed to own a gun. But, telling the dealer it's a gift often brings unnecessary hassles into the process. Most do indeed know the law and how it is applied, but I know for a fact that a good percentage of them don't. It isn't conducive to a happy gun buying experience to try to weed them out or educate them (they know the law much better than you, and will never be convinced otherwise).
As Don H's info clearly shows you can answer the question about being the actual buyer of the gun honestly, without fanfare, and move on.
As I think about it, the chain store is actually so wrong that they are trying to make what would be a legitimate purchase into a straw purchase. If you fill out the 4473 with your information, and you purchase the gun with your wife's money, then you may be breaking the law. The hazy part concerns whose money it is, if you and your wife share a bank account, as most couples do, then it might be argued that it is also your money. Bottom line is they are muddying the legal waters with their lack of knowledge of the actual laws and regulations involved.