and after exactly 1 second from dealing the last one (camera checked)
Luca, before I get into the response i just wanted to address this line. My hope is that you looked at the camera after this incident was resolved for your own education. In poker tournaments, as a TD, we have to pretend the cameras don't exist. We can't hold up a table for a floor call with the clock ticking, we can't pause the clock without holding up every table, and if we do then the tournament ends up running late. Nothing good comes from holding up the action. In a cash game you can always rack up the pot, call for review and award the pot after without other players being affected; tournaments do not allow for such an easy solution. As TD you have to use all available information, including sometimes input from the other players at the table, but surveillance can't be one of them 99.9% of the time.
As to how I would have handled the call in your original example:
If my dealer tells me that he/she completed the deal and the player was not in arms length of his chair, it's a dead hand. It doesn't matter that they grabbed the cards after; kill the hand and move on. The player can be mad, or they can choose to accept responsibility for their own action. We can't play nice, we are like referees in a sporting event, we gotta make the call and live with it. On the other hand, if the dealer says "I
think he wasn't back yet" or something that leads you to believe the player's proximity was in question, I'd favor the player but advise to not cut it so close returning to the table next time or he risks a dead hand again. Like Mike said "tie goes to the player" when it's not clear if he was in range.