You are 100% correct.

The confusion in the public stems from the fact that the news media selectively reports on recession in different ways depending on which party is in power. They ignore your fact when one party is in power and they highlight the "2 quarters of no growth" rule of thumb instead. Then when their guy is in power they go out of their way to say "Akshually a recession isn't defined by that it is defined by a committee."

Just a few examples: https://imgur.com/a/xbBzLIU