You still can't launch a rocket on US soil without a permit from the FAA, and for launches from outside of the US, I'm pretty sure that SpaceX's rocket technology is quite export controlled. But yes, it's now a bit more independent from Congress's financial mood.
My point is that there's still large government involvement. The permits are just one example. Another one would be the military contracts that require contractor employees to maintain clearance levels and create financial dependence, or the government owned launch pads they lease.
All of this combined means that SpaceX is still highly dependent from the goodwill of the US government.
