the teams need to give notification to their Conferences by the start of the first day of the 2016 fall calendar sport (which, according to a few posters, for BYU is Aug 19), after the Olympics may be too late.

It seems to me that they'd want an invite out there asap, so they can ride the headlines all the way up to the Olympics, and then issue one or three other invites during or after (depending on what the particular schools' out-clauses say) the Olympics to keep themselves somewhat in the headlines.