Hi Maggie - good morning!
A few people, like David Armano, have created models that included a fourth - the social. It might cover what you're referring to.
You're right, we DO need to see all of our communications more holistically - BUT...
The paid/earned/owned/(maybe social) is a mentail model - just a handy tool to help us, as marketers, consider aspects of what we're doing in different ways. The model CAN still be helpful for the conversation. It doesn't mean that it EXACTLY reflects reality - just that it's a tool for thinking.
Thus, I'm not sure I'd through this baby out with the bath water.