If he asked and was refused then he's justified to do so but if he went to the media before discussing it with the board, then that's another story.
I do agree with this.
I doubt if Jose would just flippantly go to the press, from the start.
I am sure that the "vibes" of not wanting to spend money are there and Jose is getting worried that he has been employed to keep the team in the top 4 (a la Arsenal), make money for the owners and not actually win anything.
Jose needs to keep the pressure on the board to spend the money, otherwise, they'll happily do the "no value in the market" thing, which they did with Fergie for several years, forcing Fergie to make do with scraps. The problem with that is that when Fergie left, we'd reached a point where we had a bunch of senior players, who were nearing departure, without any quality young players coming through the ranks.
My understanding is that the owners merely want us to retain top 4. If we drop out, it hits them financially.
If we spend an extra £300M to win the the title, we don't earn that money back, so it's best to just keep hitting top 4, on a moderate budget.
And regarding the marques signings: players which can be heavily marketed, can end up earning the club money in return.
Say if we spent £200M on Messi. We'd earn a lot of extra revenue from his signing.
But if we sign someone like Perisic. We'd probably earn nothing back in return.
So, it makes sense to spend £200M on Messi, but no sense in spending £40M on Perisic.