The intent of the straw purchase law (or at least what we're to believe is the intent) is to prevent "prohibited persons" from obtaining firearms. Unfortunately, the law is written in such a way that it criminalizes situations in which the actual buyer of the firearm is not a prohibited person.
For example, if John buys a gun and an hour later shows it to Bill who says, "nice gun, I'll give you $XXX for it" and John sells the gun to Bill, this is perfectly legal and not a straw purchase assuming that neither John nor Bill is legally prohibited from owning a gun because of a felony conviction, not being of legal age, or other such criteria for being a "prohibited person". This is legal because, at the time of the initial purchase, John was the actual buyer of the firearm and subsequently engaged in a private business transaction with his own private property.
On the other hand, if John were to call up Bill and say, "I saw this gun you might be interested in at a local shop" and Bill says "I'll send you the money to go and buy it for me" it would be a staw purchase for John to do so regardless of whether he or Bill are "prohibited persons". This is because, when John is filling out the 4473 while buying the gun, he's using Bill's money rather than his own to purchase the gun and thus is not the "actual purchaser" and therefore is lying on a federal form.
Now, if this all seems rather asinine, that's because, honestly, it is. If the intent of the law is to prevent firearms from getting into the hands of prohibited persons, then one would think that a law forbidding the knowing transfer of a firearm to a prohibited person would be sufficient. Such a law is, of course, already in force but our politicians, in their infinite wisdom, seem to think that making something "double illegal" or some other such nonsense will give pause to people who are already knowingly breaking the law. Of course, such is not the case and, as it is written, the straw purchase law serves only to turn otherwise law abiding people into (often unknowing) criminals while doing little or nothing to stop people who are already knowingly breaking the law since they obviously don't care what the law says to begin with.