No, "US Government" means government at all levels in most uses.
Anyway, regardless of your personal definition of the term, the intent of communication of the person you are replying to is crystal clear and in obvious contradiction to your analysis. (That person expressly uses the word “federal.”)
As I think about more though, I must wonder if this could be a regional thing and varies.. and or if that is relevant to the specifics in this thread.
The more I think about it, I wonder if places like Cali and NY would think of things in that manner.. with places like Texas and TN thinking very differently.
It's an interesting thought, and wonder if there is data / polls out there for something seemingly basic like this.