Dealer burns and then turns a.....face down card. He doesn't initially notice he just looks at the guy who is first to act until the table commotion turns his attention to the card.

Nobody happened to see it face up in the deck. Floor comes over and rules that it had to be a boxed card in the deck to end up face down on the table because of the way dealers flip the cards off the deck.

What do you think?

Makes sense to me, could see it going either way but if nobody could verify that the card was not boxed, I'd consider it boxed under the circumstances.

I see some dealers who like to bring out the turn/river with an unnecessary flourish, which occasionally ends up with cards face down. If it were one of these dealers I might be less confident but even then it still looks like a boxed card. I'd also remind everyone to pay closer attention.

Out of curiosity how did they handle it?

What sort of dealer doesn't look at the card when they're dealing it? Very strange...

I rarely do. I'm looking at what's coming up, not at what alread happened. Musicians don't look at their hands, either. Even when there's an exposed card and it's face-up on the stub, I rarely notice it until it's being pushed under the pot.

Is it really the players' responsibility to do this?

As a player I'm pretty much never looking at the stub. I'm either looking at the flop and might notice that the card came off upside down or I'm looking at the other player to see his reaction to the card. The chance that I'd notice a boxed card at the top of the stub before its dealt is near zero.

+1 I'm looking at other players every time I rarely watch cards get flipped on board immediately unless AI.

It's your money at risk.

When you cross a street, it's your responsibility to look both ways.

It'd be nice if the entire rest of the world were perfect and never made a mistake. But that's not reality. Even if the bus driver is at fault for running the light, you're still squished into putty when it hits you.

Protect your hand. Pay attention to everything.

It's your money at risk.

Floor said it was a "scrap, worthless piece of paper" and put into the muck which is what RROP says for boxed cards according to other posts on here. So the next card off the deck was the new turn.

Of course on the flop it was 2 pair vs. flush draw and this was the flush card so we had to hear the 2 pair guy complain for the next 30 minutes. We tried to get him to understand that it didn't really matter - you get 5 random board cards so whether it was cards 12345 or cards 56789 off the deck it was all still random. He requested over and over that the floor check the cameras to make sure it was a boxed card and not a dealer mistake, etc...but really they weren't going to ever change the ruling after the hand was over and the pot was awarded.

Adding on to what Pfapfap said, I'd add that dealers are humans and make mistakes. The only safeguard against a dealer making a mistake is a vigilant player. I rarely go a day of playing without seeing at least one dealer error that I quietly correct. Typically it's a short blind/missed ante, but sometimes it's something more significant. Almost always it's an innocent mistake, not incompetence.

Not to mention, most commonly-accepted rule sets state that players are responsible for maintaining the integrity of the game, which implicitly includes keeping tabs on the dealer.