Yes, but they investigate only specific things. Having tendrils literally everywhere (including places outside its jurisdiction) is clearly a very intrusive interpretation of their mandate.
Any good intelligence agency is going to have an information network that spans far beyond the scope of the specific things they are currently investigating, because that network takes time to build.
I actually am not sure whether that violates their mandate. Is it a problem if an agency gathers information outside their jurisdiction? Obviously they cannot make arrests, for example, but can they gather information?
Obviously they cannot make arrests, for example, but can they gather information?
In the USA, it would seem that the public laws say that the FBI can't just gather information. They are supposed to have reasonable cause, as determined by some Court. The laws and traditions demand a little oversight of information gathering, and that the information so gathered is related to a crime.
This is related to the public laws and traditions about suppression of speech, particularly political speech. Speaking freely isn't supposed to be "reasonable cause", and speaking freely isn't supposed to make you an object of surveillance. Doing otherwise "chills" free speech.
I can only conclude that the FBI has become a "rogue" agency, like the CIA has, and is full of people who have no respect for US law and tradition.