King James and Elizabeth's discussion

So that scene was well done and i think King James brought up some good points about Elizabeth being afraid. I have some questions... So James has a choice between letting his mother be excused or being the next King of England right? That was the offer? And by him not choosing his mother, Queen Elizabeth would "have no blood on her hands" (which is ironic since she's the one ordering it to be done.) Also so it would seem Elizabeth never met Mary and same for King James. Is this historically accurate?