That is not correct. Who is this “they” you are talking about? The OSI?
Open source is a term with a definition - which has been written by software freedom advocates by the way.
With free software you have politics and a philosophy, in which somebody can have more freedom or less with a piece of software. I really wouldn’t confuse that with the practicability of the OSI definition.
Copyleft or push-over is a whole separate topic. Copyleft might be favoured by software freedom enthusiasts, but I disagree with your idea of separation through that. Even if you don’t care about software freedom, you could like the practical effects of the AGPL.
I feel like you’re spreading at least misguiding information here.