If you read carefully, one reason cognitive ability is more valuable than EQ is that people with great cognitive ability can quickly learn to simulate high EQ when they need to. So EQ actually does matter, but can be simulated with general intelligence.

Anyway, I don't think the parent was talking about actual "EQ," which is a term of art that has a specific definition and measurement tools (as refenced in that article).

I think he was just saying the people who believe they are much more brilliant than all their coworkers can be hard to work with, which can cause harm to a large organization.