In which case, yes, SpaceX can also spin up new makeshift ground stations using off the shelf user terminals.
The current ground stations use specialized transceivers, but that's an efficiency improvement, not a fundamental limitation.
> I failed at that, because he probably saw that the entire concept was questionable.
There's a lesson there: if you think you understand a bleeding edge emerging technology better than Musk does, think again. Think for a long time - maximum reasoning effort.
It's not impossible that you truly are, but it is unlikely.