How do professors choose their summer salary?
I suppose this could depend on the funding agency.  For the NSF, your summer salary is determined by your academic year salary and you cannot receive more than that, although you could receive less if the program officer cuts that part of your budget.  I believe this is standard for U.S. funding agencies.

This situation is of course not fair to those who hold lower-paying jobs that do not reflect their achievements (but rather state budget priorities).  Like many things in grant funding, there's tremendous bureaucratic inertia and no hope of changing this aspect of the system.