This is a problem for beginners and world champions alike. When to convert one advantage to a material advantage and in both cases judging how effective the opponent's counterplay will be.
However nearly all players will take a free piece when the opponent has no compensation for it. Titled players even more so!
So whether or not the titled player made the right decision, if the piece seemed free to you, and they didn't take it, then you're missing the complications that scared the titled player away. A few reasons off the top of my head:
A tactic will win it back
The opponent gets a lasting initiative making the position less clear
A perpetual will make a draw
An endgame fortress makes a draw
Useful to remember is that many captures and recaptures are not forced. If the opponent makes the "obvious" capture or recapture you may be completely correct that capturing the "free" piece gives a winning position.
I should have an example for this thread, but I dont have one ready.
Not very rarely I see games where titled players got their opponent in a dangerous situation. They can take a minor piece, get an exchange or even a rook. But then they don't take the piece and instead try to make the position even tougher for the opponent by making an inbetween check, threaten another even more valuable piece... and then all of a sudden there is a save for the opponent and the attacker ends up drawn or even lost.
Titled players can often play out games 'easily' when they are a piece ahead -their opponent might even resign right away. Why pressure up even more and risk losing it all?