I'm not discounting what you heard from HR, however, I was one day of my last LOFT (finished) when I was emailed saying my background check was completed. I had a very VERY simple background. 2 addresses, 1 company prior and no recent history (20 years or more) since I had a ticket. No FAA LOI's, training issues or warnings.
I don't think anyone will know the way in which they choose who goes, but I know it's not by the time your background check is completed.
Whiskey
PS, congrats to all that have recently interviewed and/or have been hired.