That is true enough becaise SpaceX does not work like the other guys. Other companies would really halt work I doubt SpaceX will do that. Still the Starship being tested is not the lander, the design is different enough that lunar lander is going to need its own testing phase at some point. They are similar platforms for sure and I doubt SpaceX will just halt work because at the end of the day they will own the lander not sell it to NASA. NASA is paying for development and buying a ride they won't own the ship.
I still think if the Starship being tested and the Lunar Lander are different enough SpaceX might just focus on the Earth / Mars mission parts of Starship and hold work on the Lunar mission parts. The reason I say this is because the Lunar Lander is not just a simple rebranding of Starship, the Lunar lander is only designed to land on the moon, it can't return to land on Earth from the reports that have been put out. Sounds stupid but that is why SLS is there, NASA only awarded the landing part. I am pretty sure if SpaceX wanted they could create a lunar lander that could return to earth and land. This why the project is different from Starship it is being limited to do one task.
NASA calling for a halt would work on those other companies because they don't do any work without outside funding, no money, no honey. That is why they have nothing but renders and art to show.
The halt is political, and there is a chance to force NASA to make a different choice or waste money on a second provider.