How do you rule here?

[bfc]

1/2 NL at Borgata. Seat 6 has the button and I make a standard raise from seat 4. I only get 1 caller, seat 10, and we both have stacks of close to $300. The two of us see a flop, I have position, and after 30 seconds of nothing happening I notice my opponent looking at me like it's my turn to act. I ask the dealer if it's on me, she says yes, and I immediately check. My opponent then pushes, claiming he had not checked. The dealer says the bet stands and I must call it if I want to see a turn. I'm confident my opponent was not angle shooting; it's possible he was absorbed in analying the hand and it's also possible he didn't realise he was first to act. When the dealer told me it was on me I checked instantly so my opponent didn't have time to contradict her (although he could have answered me directly).

As I see it I did absolutely nothing wrong up to this point yet my opponent now has an advantage he's not entitled to. What's the relevant rule here?

I didn't call the floor because I missed the flop so badly that I didn't think it worth slowing the game to get a free look at the turn. The flop was something like 9c Tc Jc and I had 6h 7h. Would you call the floor anyway?

The thing that annoyed me most was the attitude of the dealer. There are some excellent dealers at Borgata but also some terrible ones. This dealer was not particularly interested in the game, didn't bother to gather information before ansering my question, and was not at all apologetic.