A treaty was written specifically for the rocket labs situation, and only because they were a NZ company first who were moving HQ to the US

Yes. That precedent makes it more likely that SpaceX would receive similar disposition, IMO.

RocketLab had a better reason for needing the disposition, but now that the precedent exists it opens the door to others.

But Rocket Lab don't do any military launches right? I think this is why SpaceX requires all employees to be Americans also.

RocketLab has launched US military payloads from New Zealand, but those were "R&D" payloads.

They've since built a launch facility at Wallops, Virginia to be eligible for more classified military contracts.

Presumably SpaceX would continue to launch national security payloads from US soil.

And of course advanced US government payloads have launched from French Guyana, ie James Webb.

But that's NASA, their stuff is not classified at all.