Is somehow 'in bad faith' then you're not having a discussion, you're pushing an agenda.
The dungeon master's job is to make stuff up within reasonable bounds. This includes snap judgments of "I did not establish this beforehand but because of factors I did establish, this falls within the realm of reason". If your only challenge is that something was made up and needs to be proven to have existed a priori, then no. No it does not, you're shifting the burdens around for benefit, and you're breaking the established social contract of the game.
