This is one of those cases of language running with connotations created solely from typical usage.
A very typical usage of 'must be nice' is to express some sort of judgment, or woe is me, or 'gee you're so spoiled and you don't even realize it' kind of feeling. Very much a 'wow, look at you, getting this awesome benefit - I would have liked that awesome benefit - but for some inexplicable reason, you got it and I didn't, and I'm jealous and resentful of that."
Typically, among people that I know, when someone is being passive aggressive, they say 'gee, must be nice'. When someone is being genuine, they say 'O-M-G, I am SO jealous!!" (Usually followed by "you better take pictures!!" or something.)
If I saw someone say 'must be nice' on say Facebook, without some seriously mitigating contextual usage, I would think they were most likely being passive aggressive, whiny, and a sourpuss.