Can't follow the gist of "not above 2000ft" on an FIS, if in Class G.
Is there some airspace above you that cannot be entered without clearance?
I concur, if no ATZ exists, the "lady" has no jurisdiction whatsoever. Sounds like their own pilots need to be made aware of the rules of the air. If you fly in the open FIR, that's exactly what it is.
Having said that, can't you give them some lateral avoidance?