Foul Tip or Foul Ball?

 
With a 2-2 count, the batter swings and tips the pitch straight back to the catcher. The ball goes from the bat to the catcher's thigh and rolls to the catcher's stomach. The catcher grabs the ball and holds it up to show to the plate umpire. 
 
The defensive coach thinks this is a caught third-strike foul-tip. The tip went directly to the catcher and then the catcher clearly secured the ball without the ball ever touching the ground.
 
Is the batter out on strike-3 or does the batter remain at bat with a 2-2 count?
 
Call
A foul tip is a batted ball that goes sharply/directly from the bat to either of the catcher's hands and is then legally caught by the catcher. A strike is called and the ball stays live (NF 2-16-1).
 
In the play below, the tipped pitch first went to the catcher's body and then was secured by the catcher. This is not a foul-tip. It is a foul ball (see NF casebook 2.16.2A).