Another way to phrase that first sentence is "assumption of innocence". And while random commentators on the internet are not obligated to honor it, law enforcement is supposed to.
Presumption of innocence does not extend to the initiation of an investigation, but comes into play with increasingly invasive methods (and ultimately, charges).
US law enforcement is empowered to initiate duck investigations on things that quack pretty liberally.
If your in some group that reenacts pointing weapons at each other, or coming up with idea on how to blow up buildings and you have someone overhear this and report it, law enforcement themselves have no idea if you're the real thing our not (statistically, no your not, but investigators deal with outliers all day every day). If there is some kind of audio or video evidence saying something actionable (even though it may be pretend) and that gets in front of a judge, expect a warrant to get issued to tap into just about every part of your life.
This is not the standard actually applied to law enforcement in the US. You can be convicted of nothing other than resisting arrest. Resisting arrest for what? Literally does not matter.
Also if you are arrested and found innocent, you are not compensated in any way for that arrest, which was clearly wrongful. Police in general are simply exempt from unlawful detention, except in cases of a well connected individual.
Not only that, there are likely fees and fines.