Right you are, but... the Falcons held the #10 pick in the '95 draft. The Browns traded Eric Metcalf, and their first round pick (#26-Devin Bush) to the Falcons for their 1st round pick (#10-J.J. Stokes) on 1995-03-25. The the 49ers traded their first round pick (#30-Craig Powell), their third round pick (#94-Mike Frederick), fourth round pick (#119-Dave Barr), and '96 first round pick (#26 overall) to Browns for the tenth pick which turned out to be JJ Stokes.
Basically, Belichick traded JJ Stokes for Craig Powell, Mike Frederick, Dave Barr and the 49ers '96 first rounder. It gets better.
Belichick was fired by the Browns and went back to work with Parcells in New England leaving the Browns with the 26th pick in the 1st round of the 1996 draft which happened to be linebacker Ray Lewis. The Browns moved to Baltimore and became the Ravens.
In 1996 Bill Belichick landed on his feet as defensive coordinator of the New England Patriots who went to Super Bowl 31 and lost to Brett Favre and Reggie White and the Green Bay Packers.
Doesn't read much like Bill Belichick had a thing for Warren Sapp in all of that. Like I said, Sapp is a moron.