Jclough,
While your post doesn't clearly define your problem, I think you can both be partially correct.
Will placing shelving feet on small steel plates reduce the change of overloading our concrete mezzanine?
Not necessarily. The load will still be present on the mezzanine, no matter how you try and distribute it.
However, the steel plate should help distribute the weight over a larger portion of concrete. If the failure mode is punching shear, then yes, a plate would help, but you would have to design the plate correctly. If the failure mode is bending, the no, you would need something to distribute the load to a framing member. Other failure modes might require other solutions also.
More information would be needed to help diagnose your situation.