I’ve never heard anything about the Boy Scouts refusing to admit gay scouts—I’ve just heard they didn’t want gay scout leaders. But then it’s hard for me to wrap my mind around a scout being sexually active, much less homosexually active. I would think any kind of sexual activity outside marriage would violate the oath of a Scout.
To the best of my knowledge they do not. Your memory is correct concerning gay Scout leaders. There was a controversy awhile back about admitting Scouts who were avowed atheists due to the "Brave, Clean, Reverent" credo - possibly people are conflating the two issues.
As of 2003, the ban was on Scouts in general, not just leaders. From a June 9th, 2003, press release/position statement on the BSA National Council site:
Applications for leadership and membership do not inquire into sexual orientation. However, an individual who declares himself to be a homosexual would not be permitted to join Scouting. All members in Scouting must affirm the values of the Scout Oath and Law, and all leaders must be able to model those values for youth.