It depends on the scanner, camera, how steady your hands are, lighting condition, etc.
Unless you have a pretty old scanner or there's something wrong with it, I don't see why you should change your system based on that scheduler's opinion.
The issue is whether the document clarity is acceptable with your scanner and not whether the document clarity may improve with a camera phone. I'm pretty sure the scheduler is not offering to pay for a camera phone for you.
If you have a camera phone already, you can always experiment.