The most they can typically get is the "typical" salary for a given position at a large company. There are exceptions of course, and the good ole' boys network can sometimes run deep.
But in the end, if you are let go or not hired because you lied about a salary they were otherwise willing to pay you? You dodged a bullet. Who would want to work in such an environment to begin with?
The correct answer is to say with what you think the current position is worth and what you want to get paid. There is no upside to being truthful here.
This is legitimately hard for a lot of folks to understand, the same type of folks who equate violating corporate policy as being "illegal".
I'd even go so far to say it's close to immoral not to lie on this question given the power imbalance when it comes to hiring.