Launching to Earth orbit has a clear business plan. Companies with real revenue streams will pay for this service for sound business reasons. Thus, it makes sense for a private company to do this. They can make money this way and that is what all business are out to do.
Going to Mars, though, does not have a clear plan. Where is the profit? Even if you can do it for a reasonable cost, how do you make money? Thus, I'm sure many in NASA and outside, are doubtful that Musk will actually do this.
However, if Elon Musk does send humans to Mars then funding NASA to do the same thing is an expensive redundancy. If enough of Congress believes that story then there will be no funding for NASA.
If Elon Musk does not go to Mars and NASA does not go to Mars (because congress thought Elon Musk would do it) then I guess nobody goes to Mars.
That is the sort wariness I would expect from smart people working at NASA.