The theory is if say you have 1000Hz (report every 1ms) and your opponent is on 125Hz (report every 8ms), if you both click at the same time, your opponent's input may be delayed further than yours. So supposedly this gets into the computer faster, then gets shoved out to the world faster, which the server then receives before the other's.
So originally I thought "this only really matters if the client timestamps their packets and sends it to the server", which to me sounds iffy because 1. can you really trust the client and 2. what about clock drift? But apparently there are ways to accurately sync time across a network, so assuming the server and clients are all synced, being able to send out your command sooner could make a difference. And this is without regards to network latency, since any competent online game's server code would account for this.
However the only other issue is how the server processes client state. Most games still use a tick based system which means they only process everyone's state in discrete intervals. This could mean that even if your command technically arrived first, it'll be lumped in the same processing tick and as far as the server's concerned, you both shot at the same time.
tl;dr, polling rate is more to make sure your commands get out sooner. It doesn't affect how the mouse "feels" terms of movement or whatnot.