Should fans bother players while out in public?

A few weeks ago, my wife and I, along with our good friend, went to the Xcel Energy Center for an impromptu Sunday afternoon Minnesota Frost game.
I had never been to a Frost game, and we have been talking about catching a game since last year. With it being a decently nice day for the winter time, it felt like a perfect opportunity to catch a game.
Before I get any further, I must say it was a great game, and definitely a fun experience. If you haven’t been to a game yet, I highly suggest attending sometime.
After the game, we decided to get a bite to eat, so naturally we took the sky way to avoid the cold, and made our way over to the Pillbox Tavern.
We were there for a while, catching the rest of one of the playoff football games, when our friend noticed some of the Frost players were sitting at a table near us.
This instantly prompted the debate of whether or not going over and talking to them was a nice thing to do or not.
On the one hand, after playing in a professional game, I am sure getting some food and maybe a drink in peace is something most players enjoy.
On the other hand, professional athletes generally love their fans, and I am sure it feels good when they come up to them and say “good game” or something to that effect.
We ended up deciding not to say anything which then prompted another 10 minute debate in the Uber ride back to my house.
So the question is did we make the right decision?