[BoomerSooner]

I don't have my books, but my thinking is that any player that is not already in the game, DQ'ed, or ejected is an eligible substitute. I don't think there is any wording that declares that a replaced player is an "ineligible substitute", but rather there are restrictions on when s/he can reenter. In this case the restriction is after the clock has started.

If this logic is acceptable, then the wording of rule in question says that any eligible substitute my take an injured players free-throws. The use of the word any implies an exception ot the previous restriction.

Essentially my reasoning is that while the the rule allowing the substitute to shoot the FT's is providing permission for any eligible substitute to enter given the sitution of an injury. Ultimately it is my belief that given that the rule specifically addresses a specific situation (what to do with an injured player's FT's) and gives a direct solution to said situation with the permissive phrase of "any eligible sub", the specific situation ruling should take precedence over the general restriction on re-entering a replaced player. It's similar to telling your kids not to go outside after dark (general rule), but that if there is a fire they should go outside immediately (specific situation).

This is just my opinion and since I'm away from my rule book, I don't have the exact wording of the rule, I reserve the right to change my opinion. In the end it will come down to the exact definition of "eligible substitute".