Quoting the entire paragraph doesn't alter the fact that you claim the right to decide who is pilot in command; it is not your right to make this decision except for on your own aeroplanes! When you turn up to hire an aeroplane the owner/operator has a legal duty to nominate a pilot in command; some may chose you, some may not but, who ever is the nominated pilot in command logs the time as P1, that's the law!
A good instructor can often recognise a muppet even before they get near the aeroplane but if, as FFF suggests you have got airborne in the rented aeroplane and the instructor feels the need to take control he can not do so legally unless he is the pilot in command. If you are the pilot in command and he tries to take over without your apporoval he is comitting a serious criminal offence! Some operators and instructors may be happy putting themselves in that situation, I am not and I choose not to do it.
If I fly on a check out with a pilot I don't know, I am pilot in command or I stay on the ground.
See Ya!