I think this may be a line. I've researched the S.M.A.R.T program, and can not find anywhere in the policies which specify a referral must enlist within 7 days. Here is a link to the programs policies, and with some navigating you can get more info on the program itself. The only way his buddy can miss out on the bonus is if the referral (your brother) does not enlist, is not qualified to enlist, or enlists but does not complete IET. (BCT/AIT)
http://www.usarec.army.mil/smart/policies.htm