I think it's a much greater stretch to pretend that this person's obvious political bias doesn't leak into the "fact checking" they choose to do - or not to do, which is kind of the bigger issue. They may "correctly", ignoring the philosophically charged issue of "correct", fact check a certain politician but choose to ignore a different politician's statements that would otherwise be noted as incorrect under the same or similar standard.
Twitter obviously has double standards; has for years. Remember when the US elected a troll and Twitter responded to calls they enforce their own TOS by modifying the TOS to have a carve-out for "newsworthiness?"
ha oh, in that case that's a bit of an own goal from Twitter.
Although I doubt he put that fact checking warning up all on his own, there must have been a policy in place that senior management agreed to, and legal have presumably okayed.