Are they giving instructions or making suggestions?
They're making suggestions.
My recollection is that you can fly in someone's ATZ if you have sufficient information to ensure the safety of the flight. If they say "it's a bit busy in here, we'd rather you kept clear" I don't mind going a mile or two to one side or the other.
It's no big deal to pick up the VOR radial or the magenta line again once I'm past. Or, I could even look out the window.