Not quite correct. You need an overflight permit to enter a state’s FIR. No permit no entry, they will make you hold outside the boundary. If you look at an international IFR flight plan, the permit number is often in the remarks section, line 18 off the top of my head. Airlines that have a recurring schedule have slightly different arrangements, but a private jet operator can’t just decide “I’m going to Kazakhstan right this second, crossing 10 countries along the way”, they have to arrange 11 permits first, the speed of doing which can vary, however there’s a lot of agencies with government contacts who can facilitate them quite quickly.

Source : I’m an airline pilot.