If you ask Google to define "supposedly" it says: "according to what is generally assumed or believed (often used to indicate that the speaker doubts the truth of the statement)."
I hate these sort of semantic arguments. In case my sentence was not clear, I don't support the things that have been done to people under the guise of "Gamergate", I don't think she slept with anyone (nor do I care nor see why it is relevant), I don't think Kotaku gave the game good press because of the "alleged" romantic relationship, I honestly I don't give a shit about any of it, and I feel like I lost "the game" by even attempting to casually engage with this dumb fucking topic in any way.
Hey man, i'm not criticizing you. You're making a good point. I want to make that point even stronger.
It's not semantics in the sense that we're quibbling over the definition of words. Your point can be even more definitive. Gamergaters are claiming something that is not true.
It doesn't matter if Gamergaters believe it to be true. It's not. <3