It may well be the crown, but my first watch and a number of others that I've read of have a "wobbly" side button. I can see where that might result in a rattle if the watch vibrates. I really don't see how the crown could. Can you move the crown by applying a very light pressure with your finger back and forth on it? Try that also on the side button. Mine was wobbly enough that I had trouble launching Apple Pay with the double push so they replaced it for me.
The side button does have a bit of wobble to it, but nothing to the point that it makes it hard for the watch to register the double push. It's comparable to the wiggle of the lock button that many people with an iPhone have experienced (after two generations of iPhones with a slightly wobbly lock button, that's what I presume). Putting gentle pressure on that doesn't stop the rattling.
I've felt that the vibration on my watch has been somewhat weak, hopefully it isn't a telltale sign of a failing Taptic Engine!
