I have no interest in a keeper league, but Yahoo Roto leagues (with no H2H element) can start same day if you set to Daily - Today. You actually could have scored today's game if you completed draft before the first game today.
If does have a H2H element, I believe you correct there.....and can't start season til Oct 28. (I'm less certain of this as I only play Roto w/o any H2H element)
They make it confusing the various things they indicate between the different formats on the site, but there's a big orange banner on Yahoo league homepages that states:
"To score for the entire NBA season, leagues with Daily - Today roster changes must complete their draft by October 22nd before the start of the first game. However, Daily - Tomorrow and Weekly leagues must complete their live draft by October 21st at 11:59pm PT"