Top speed of 20mph specifically means that the electric assist cuts out at 20mph, and you're correct in assessing the reason. If you want to go over 20mph, you either need to do it with pedal power or get registered as a motorcycle.
Not true. The Specialized Turbo goes up to 45 km/h with some assist.
" e-bikes must have a motor of less than 750 watts and an unassisted speed of less than 20 mph. Because the Turbo is an electric pedal-assist bike, meaning you have to pedal to get any kick from the motor, the speed limit doesn’t apply. In fact, the only reason it tops out at 28 mph is to comply with European laws, which restrict e-bikes to 45 kph. Specialized installed a governor on the Turbo that automatically turns the motor off when it reaches this speed."
"European Union directive 2002/24/EC exempts vehicles with the following definition from type approval: 'Cycles with pedal assistance which are equipped with an auxiliary electric motor having a maximum continuous rated power of 0.25 kW, of which the output is progressively reduced and finally cut off as the vehicle reaches a speed of 25 km/h or if the cyclist stops pedaling.'"
Being a bike means (depending on the country) that you have to use a helmet, insurance, drivers license, cannot ride on an optional cycle lane, etc.