I imagine that doesn't matter. I can't imagine that people who would actually buy their services would not actually know the difference, so I don't see this as a big marketing/PR hit. It's not like the people who would buy these services are clueless managers who make bad IT investments. The people who'd buy these services or make investments (e.g. NASA) would know the difference as to what's what.

But, to the public who elects the representatives who control the budgets of the agencies that make the investments, it does matter. It can be critical.

We have people elected congress who don't believe in things like evolution or climate change, which affects national policy, budgets, and investments. Same thing.

Or just the representatives themselves. How long will it be before some Congressmoron asks, "Why are we giving Elon Musk $300 million to take our people to the space station when Amazon is doing the same thing for $3 million?"

I think PR for "normal people" absolutely matters when it comes to Elon Musk and his companies' reputation.