While the most well known, there are other points of presence doing the same thing. Easy and trivial to duplicate traffic at line speed. It doesn't affect the traffic flow itself.
Yes you can trivially tap a fibre -- https://www.gigamon.com/products/access-traffic/network-taps... for example
You can even do this without breaking the fibre
What you can't do is ship 80% of the traffic across the world to the US without either the ISPs agreeing, and thus a conspiracy of thousands of people in thousands of ISPs, or doing it outside the data centres, meaning millions of taps in various ducts around the globe, which would be found on a daily basis.
They will never believe you until you show them and that requires a clearance.