http://www.ncaapublications.com/productd...s/BR19.pdf matches what I said earlier and says:

"Section 3. Who Attempts
Art. 1. Personal fouls—The free throw(s) awarded because of a personal foul
shall be attempted by the offended player, unless one of the conditions of Article
2 or 3 of this section are met.
Art 2. The free throw(s) that were to be attempted by the offended player
shall be attempted by that player’s substitute unless no substitute is available, in
which case any team member shall attempt the free throw(s) when the offended
player is disqualified or ejected or must withdraw because he is bleeding or has blood
on his uniform or person, or when a player is withdrawn because of a lost,
displaced or irritated contact lens.
Art. 3. When an injured player is unable to attempt a free throw try(s), the head
coach from the opposing team shall select one of the four remaining players on
the playing court to attempt the free throw try(s). When a foul is flagrant and
the injured player is unable to attempt free throw try(s), the injured player's
head coach shall select any player or team member to attempt the free throw
try(s). When the injured player is bleeding, his head coach may: 1) provide a
substitute for the bleeding player who will attempt the free throw try(s), or 2)
request a timeout and attempt to remedy the blood situation. (See Rule 3-6.3.f)"

Based on Article 2, Brantley's replacement had to shoot free throws after Brantley fouled out. Any player can sub in for Brantley, but none of four players remaining in can shoot free throws.