Both Nute and Local Garrison say "to a minimum of 1," so your opponent will still get a resource.

Ah missed the minimum on Nute, good catch

Oh another thing the Traitor is going to piss off: Cad Bane lists

You must ACTIVATE HIM as your next action. Meaning you cant use his special action since thats not "activate a character" thats "use the action on a card"
Sabine gets off since her ability is when she activates