I don’t think I’d characterize it as misleading. Obviously, Labour is trying to do some damage control, but Starmer said what he said, and more importantly, he tolerates extremist transphobes in the party and rarely if ever speaks up when they go on the attack.
LGBTQ people, including several I know, are fleeing Labour because they identify it as the party of transphobia.
One of my best friends, whom I would have previously described as a Labour fanatic, voted Green for the first time in the recent by-elections. He says he’ll never vote Labour again. I don’t know if he’ll change his mind, but he can’t stand how transphobic the party has become.