alpha max
Alpha max protects against stalling.
During take-off roll, a-max protection is not active, pitch control is direct (pull stick x amount, get elevator x amount, i.e. not y amount as modulated by flight control computer.
But anyway, contact of tail with ground occurs at lower angle than angle at which wing would stall.
PBL's puzzle is much about well, when flying and you pull, than angle of attack increases, so lift increases, so aircraft moves away from earth, so tail cannot hit earth anymore. But, as aircraft rotates, approximately around the wings, the initial movement of the tail is still down - during a take-off, the point of closest proximity of belly underside to runway occurs just after main wheels have lifted off! (at least with long aircraft).
I cannot quickly calculate anything to solve PBL's puzzle, but I hope some mysterious concepts have been cleared up.