I'm a programmer from NMRiH on the Source engine. I suspect their animation system is vastly different than the one we received for our game since the games are rooted off different versions of the engine. However, I also suspect this is a very easy fix introduced by the foot-locking or left baked in as a network-traffic reduction.

Anyone who has played for more than 5 years remembers when you used to be able to aim 90 degrees to the right of where you were actually looking by very slowly aiming that direction in small increments and I think we're working with a similar bug here. The view-angle is not networked to all users unless a minimum X degree movement is sent, afterwhich it seems to network it consistently.

Barring a bug in the animation logic or worse the network logic which would be preventing the delivery of eye position updates to the clients, it should be as easy as upping the update rate of the eye position variable to all clients, especially when another client is looking at them.