I think that's naive. The parent comment phrases it a bit more cynically than I would have, but it's in everyone's best interests to casually document plans and intentions. People forget, people misremember, people promise things without fully thinking through the implications in the moment. A friendly email restating the key points of a discussion is conscientious, professional, and keeps everyone on the same page.

I'd personally be very suspicious of anyone who tells you not to do that. There is literally no downside unless you're trying to hide something.