There's no need to shame people who are wrong.
While there is perhaps no need to shame someone who is acting in a shameful way, I find it hard to criticize someone for doing so. Sometimes an aggressive statement deserves an aggressive response.
Or, to defer to the ever-wise Gods of the Copybook Headings:
"What's good for the goose is good for the gander".
1: https://en.wiktionary.org/wiki/what%27s_sauce_for_the_goose_...
I've been in this situation before and I've found this approach beneficial.
Some do, some think it is a sign of weakness and start behaving even more unreasonably.
But it's necessary to shame people who work the trade desks, or else they will never learn.