I realize the following seems like a distinction without a difference: however, although you may legally give your brother a pistol you cannot purchase it for him.
The distinction stems from the ATF using undercover agents to bust FFL dealers. The agents lead the dealer into believing that they want to make a straw purchase. The reality is that both agents could legally buy the handgun but they make the dealer believe otherwise. Therefore, for all practical purposes a straw purchase is no longer simply buying for a prohibited person, but rather the intended purchaser must be the actual purchaser to avoid a straw purchase.
This allows prosecution of FFL dealers who demonstrate the willingness and intent to engage in a straw purchase, even when none of the parties to the sale are prohibited persons. Personally, I think it is a heavy-handed tactic and not necessary to catch the few dealers who engage in questionable business dealings.
Also be aware that State law varies (e.g. it is illegal for anyone under the age of 21 to possess a handgun in South Carolina).
Therefore, to answer your question directly, unless your brother is prohibited from possessing a handgun, you may legally give him a handgun.