[Sonar5]

You Said:
"it looks like the catcher got the mitt underneath the ball.
Another way to say that is catching the ball.
Still, a guy cannot run out of the baseline."

Please Go read a baseball rule book. You have no idea what you are talking about.

[tallhappy]

In this play - if in fact it had been caught on the bounce (which it wasn't)-- it is exactly as if it was in play the same as if it were a bunt or weak ground ball etc...

The batter cannot run around foul territory going to first.

Going to first one has to go in the base line.