If I understand it right, if a necromancer plays a Band of Misfits from the trash, and that Band of Misfits plays a Throne Room from the supply, and that Throne Room plays a duration, the Necromancer also stays out, correct? The Band of Misfits would have stayed out since the Throne Room it plays would have, and the Necromancer stays out because the Band of Misfits it plays would have stayed out.
Exactly (under the assumption that the Duration stays out). If you want to find out if a given card stays out, you apply the rules 'forward' (Is the card a Duartion, Throne-like or BoM-like? If yes, look if the rule for it applies, and if it is a Throne- or BoM-like, that will involve looking at the card(s) it played, recursively). In this case:
Necromancer plays Band of Misfits, stays out if Band of Misfits would stay out.
Band of Misfits plays Throne Room, stays out if Throne Room would stay out.
Throne Room plays Duration, stays out if Duration stays out.
Duration stays out (directly determined by the effect it has, or maybe other criteria if it is a BoM-like as well (Captain))
So if the Duration stays out, so will Necromancer, Band of Misfits and Throne Room.