The way that weasels (BTW: The Way of the Weasel, by Scott Adams, is downright prophetic about this kind of stuff) deal with it, is to not respond at all. Then, when you bring it up, they say “I never agreed to/said that!” If you then share the email, they say “I never got that. I would have corrected it, if I had.”
Their manager always has their back on these exchanges.