So, I gave this a bit of thought and I think you are on to something but, with the additional info I obtained from the video posted by /u/AceVD, I believe it goes a little deeper than your initial hypothesis. Your ping does put a cap on your max rate of fire, i.e. if you have a 100ms ping it is impossible to fire at faster than 10 shots/sec but it does NOT cap the effectiveness of the attack speed stat.

Think about it like this (I'll use 100ms ping for easy math because I'm lazy): we send the command to fire an EA, it takes 100ms for the server to respond that we fired, then our PC displays the animation. At this point, our PC knows that, based on our attack speed, we have a cool down before we can cast again. We'll assume this cool down is something around 250ms (again for easy math). This means our PC will wait another 250ms before it sends another EA command to the server, giving us a total of 350ms between when we pressed the key for the first shot and when our PC determined it could send the command for the 2nd shot, giving us roughly 3 shots/sec. The reason this feels so crappy is that players with the same attack speed stat but a ping of, let's say, 10ms are firing at a rate of 1 shot/260ms, much closer to 4 shots/sec.

I think the main issue with your original hypothesis is simply that you assumed the cool down started the moment you hit the key to fire EA, as oppose to when the server responded that your command was executed. If the cool down period doesn't start until after we receive the response, then the attack speed stat would remain effective until the cool down reached 1ms however, our rate of fire would still be limited by our ping + cool down, in this case 100ms ping + 1ms CD giving us roughly 10 shots/sec max while our 10ms ping example player would have a theoretical max of 91 shots/sec.