Not true. You are supposed to present possession of the ball to indicate that you caught it and had control. The fact that Varitek had possession of the ball and dropped it after the tag is of no consquence because he was running with the ball and not catching the ball prior to the tag. Here are the official definitions of “TAG” and “CATCH” from MLB (notice it says nothing about presenting the ball on a tag):

A TAG is the action of a fielder in touching a base with his body while holding the
ball securely and firmly in his hand or glove; or touching a runner with the ball, or with his
hand or glove holding the ball, while holding the ball securely and firmly in his hand or
glove.

A CATCH is the act of a fielder in getting secure possession in his hand or glove of
a ball in flight and firmly holding it; providing he does not use his cap, protector, pocket or
any other part of his uniform in getting possession. It is not a catch, however, if
simultaneously or immediately following his contact with the ball, he collides with a player,
or with a wall, or if he falls down, and as a result of such collision or falling, drops the ball.
It is not a catch if a fielder touches a fly ball which then hits a member of the offensive team
or an umpire and then is caught by another defensive player. If the fielder has made the
catch and drops the ball while in the act of making a throw following the catch, the ball shall
be adjudged to have been caught. In establishing the validity of the catch, the fielder shall
hold the ball long enough to prove that he has complete control of the ball and that his
release of the ball is voluntary and intentional.