Are US PhD admission offers binding?

So I have just accepted (via some online function on the website) an offer of PhD admission into a prestigious US university. I have also been in telephonic and email contact with staff at this university. I still feel like it is rather informal. The department told me more information would arrive in April.

What I want to know is, is the offer I have accepted binding on the part of university? I have (and am about to decline) concrete offers from some UK groups and I am worried that I will be burning bridges. Can a US university rescind their offer? Does this ever happen? Am I just being paranoid?

For example, as I am still in master's program, my other offers usually said that I was admitted on the condition that I obtained a sufficiently good grade in my degree etc. My US offer does not make mention of anything like this - not that I plan on doing badly but it is good to know. Would the department think it odd if I asked along these lines?