I think there's a misunderstanding of the new format and what the real limitation is. It has been assumed by some that in a 15-team tourney there will only be one bye, for the top seed. That would be true if #1 played #16, 2 vs 15, etc. But that would require playing 8 games in a day, and we're limited to four per day. To wrap your brain around the schedule, work backwards from Friday (the first normal day with four games and seeds 1-8). You can only add 4 teams per day, so Thursday adds seeds 9-12 playing 5-8 for their slots. Wednesday could potentially add seeds 13-16 playing 9-12 for their slots, but here's where the extra bye comes into play - the ninth-seeded team gets a break for finishing in the top half during the regular season.
To add the three leftovers you'd either need yet another day or you'd have to add a fifth game on Wed and Thurs, with the 4 seed playing on Thurs. It'd be hard to squeeze in a fifth game, you'd lose the dinner break and still have a 14-hour day.