Is it more the PCs or "eyes" job to look for card counters? In my experience, the majority of the times I've gotten heat or backed off was from doing something careless/stupid when the PC was watching.
Outside of Vegas, I've seen maybe two smart pit bosses. And my guess is that only every tenth surveillance person is sharp. No idea how it is in Vegas.
The Pit Critters are generally required to "pick up the phone" and have surveillance make the decision. If they decide to back you off (or worse) the casino shift manager is the person who generally gives you "the tap"
It was my understanding that in most (larger) places the pit may notice something, and alert the eye, who then studies the play and makes the decision.