It's technically possible to build battery packs that can accept very high charge rates. Tesla has done this with the Model S pack (1.3C - 2C), but it's certainly possible to do this with a smaller battery pack as well. I fully expect the ~50 kWh Model E pack to be able to accept the fully 135 kW charge rate (2.5 - 3C).
The other point they miss is that miles per minute is a terrible metric for the same reason miles per gallon is a terrible metric.
Going from 20 mpg to 30 mpg is a greater reduction in fuel consumption than going from 30 mpg to 50 mpg.
Likewise, 6 miles per minute sounds much, much worse than 150 miles per minute. And it is, the gas fill rate is much much faster. But you save more time going from 6 miles/min to 12 miles/min than from 12 miles/min to 150 miles/min.
Look at it another way:
Assume a 70 mile trip @ 70 mph.
Add 5 minutes to each trip to account for pulling off the highway, plugging in, etc.
Gas scenario:
60 minutes of driving. 5 minutes to pull over. 0.5 minutes to refuel. 65.5 minutes total.
EV scenario:
60 minutes of driving. 5 minutes to pull over. 12 minutes to refuel. 77 minutes total.
The EV scenario is "only" 17% longer, even though gas is 30x faster to fill.
And in practice, since usually the EV will start full from an overnight trip, shorter trips will look like this:
Gas scenario:
120 minutes to drive 140 miles. 5 minutes to pull over. 5 minutes to fill up, pay your $15, etc. 130 minutes total.
EV scenario:
120 minutes to drive 140 miles. 10 seconds to unplug at the start and replug at the destination.