It's not the stupidest argument, but it applies to every last staff member of the us treasury.
None of the bureaucrats are elected, and this data has been gathered by the government to perform its functions. Insofar as Elon's team are pretty much just a couple of new bureaucrats bought in by Trump; they can use this data to streamline government. The office of president is pretty powerful; odds are he can appoint people to do work for him. It'd be crazy if he can't.
The problem is the government shouldn't be storing a whole bunch of sensitive data. It is like being shocked that someone in the NSA is actually looking at all the data they collect - there is a big problem there, but it is that they're collecting and storing the data. Obviously once they have it people will look at it. That is why it is being gathered and stored. It should be criminal to store on the grounds of privacy; but it isn't.