soup, you hit it right. Spanky ... sounds like you're either in a government or mega-corp situation.
IMHO, one should always negotiate for the highest comp possible ... you won't often have a better opportunity after they hire you.
The first one to name a number in compensation discussions usually loses. Business owners and CEO's do not tell vendors what they're willing to pay, or what they are paying now for a current good or service ... it is considered very foolish.
Same with comp. But your ability to hold out will depend upon your situation. [Another good reason for FI] If you're desperate for that job, then you may need to cave in before they do ... but if you do, try to at least make the number as high as reasonably possible ... include everything in your number. Salary, bonus, any 401k match, etc.
This is something employers do because we can get away with it, and it reduces our costs. And, managing our costs ... especially the very large cost of compensation ... is an important part of managing a business.
As much as possible, I think candidates are best off to keep their current comp close to their vest, and to seek more variable compensation plans. I much prefer a low salary, but a large bonus potential based upon output and performance. Some jobs lend themselves to this, many don't. When they keep asking about current compensation, just say you consider that confidential, and you are only seeking market comp for the job at hand, and recognition for your actual performance on the job.
A big problem when we're hired below market is that it is so tough to recover. If going comp is $75K, but we're hired in at $50K because our former employer was a tightwad ... then we need a 50% raise just to get back to market. Pretty tough to accomplish. Frankly, I've see people lie about their comp in such a situation, with success. Not suggesting anyone lie, but ... sometimes fire must be fought with fire ...
Best of luck.