No, because the injury RATE is the number of injuries divided by hours worked.

More rockets = more people working more hours.

It's not about the rockets built. It's about the city being built. It's the welders and the framers and the roofers and the concrete workers and the jackhammer guys and the linemen and the plumbers, etc. that are leading the injuries, not the guys on the line building the actual ships and boosters. Starbase is a city, not just a factory.

Those people are not SpaceX employees

Conversely, they make more rockets than any competitor, so they should be better at doing it without injury.

why would that be?

No real reason. Just pointing out that the parent argument cuts both ways.

No, that would justify a higher absolute count of injuries. If the rate is higher, it's less safe.

So SpaceX could improve their numbers by hiring a bunch of people that do nothing but make useless PowerPoints.

Yes, that is how rates work