Rozier was drafted so that Ainge could trade Isaiah Thomas further down the road.
I don't really think this is how Ainge drafts.
I think Rozier was taken because Ainge went through his first, second, and third options -- trading up to the top of the draft (Okafor), trading into the top 10 (Winslow), trading a few spots up to take a wing with upside (Oubre) -- and found himself sitting at #16 despite his best efforts.
At that spot, he went with the type of player he felt most confident projecting to the NBA: a shooting-deficient, defense-first combo guard. In short, a prototypical Ainge pick.
In that situation, left with a selection of less than ideal options, the "best player available" was the one he felt most comfortable betting on to making it as a role player at the NBA level.