I call it a bluff because the implication is it's non-negotiable. One of the reasons I say this is that if people weren't falling for it, they wouldn't tell yo

I call it a bluff because the implication is it's non-negotiable. One of the reasons I say this is that if people weren't falling for it, they wouldn't tell you they're applying an adjustment at all, because it tells you their actual budget is higher. They'd just give you a lower number and leave it at that. If they go so far as to communicate the amount of your adjustment, they're making a particularly poor strategic move because it tells you exactly how much higher their lower bound really is.