But that may not always be obvious to people - in my case, for some reason I worry about my future manager "seeing" me in a negative way. Or perhaps they will decide that I'm not a team player and revoke the offer.

What makes it completely loony, is that I have been the manager, and I never looked at it that way. But yet, I assume everyone else has a very different view of things than I do.

Yeah, but there's a perceived risk.

According to who? When in the position of counter-offering, it feels to most people like it's extremely risky. Risk in this context isn't about actual danger, it's about how much danger is perceived.