It’s not inaccurate at all. He voted against a Conservative motion to rethink expansion plans and with the government. I do not see how you can interpret that as anything but a vote in support of the government. You might just be able to argue that if he’d abstained, but he didn’t he voted for the government and against what he proports are his anti-expansion principles.
I’m not sure what you mean by you second point. I don’t put emails on here, if that’s what you mean.