Here's a good Physics SE answer that addresses this point. The "electrons move slowly in a wire" is a hypercorrection, similar to "light slows down is glass": https://physics.stackexchange.com/a/13568.
Parent didn't say electrons move slowly. Parent said electron flow is slow which is true. The article tries to say that in that average there are fast-moving parts and slow-moving parts. Fine.
No, that's the wrong interpretation. The truth is that there is no such thing as "electron flow". It's not a quantum mechanical concept, just a classical approximation.
