I'm not believing that, and I don't think other people believe it if they think about it, but the big unanswered question is how much difference is there?
It stands to reason that if you have an electric blender it will take a certain amount of electricity for a certain task. I've worked on some water pump systems that use 3000 hp electric motors, lets put one of those on a stand and put the blender mechanism on the end of it. Will it make the same milkshake with the same amount of electricity as the original blender? I don't think it will, I'm not sure if the amount of electricity used by the original blender would even rotate the 3000hp motor.
Going back to this picture:
Top speed on a Leaf is around 106 mph, so let's just make the math simple and say that 10,000 RPM on the motor is 100 mph by the time you do all the math on the reduction ratio and tire diameter. It's probably a little lower RPM for that speed, but close enough. Off the line to ~25-30 MPH, you're limited by motor torque rather than total output power, as the motor goes from 80-ish% efficiency to 88% or so. At that point, torque goes down on a constant-hp curve until you hit top efficiency at ~60 mph. That matches my driving experience that it's really fast off the line and then starts getting less oomph around 35-40 mph. For the record, the Leaf's 0-60 is a relatively sedate 7.4 seconds.
To take a less extreme version of the fractional-hp-blender-vs-3000-hp-water-pump analogy, let's assume you put the same motor in an electric go-kart that's 1/4 the weight and drag of a Leaf, but has the same reduction ratio and wheel diameter. The go-kart would have supercar-like performance, with 0-60 to match a Tesla Plaid, likely limited by how well you can stick the tires to the pavement. If you put the Leaf next to the go-kart and had them both run a 0-60 but with the go-kart running at the same speed as the Leaf, the go-kart would use roughly 1/4 of the total kWh as the Leaf in the race. It would be a little more than 1/4 since the go-kart would likely be in a slightly less efficient range of motor power output, around 92% efficiency at 60 mph.
To finish out our thought experiment, now get a second go-kart that has a motor 1/4 of the horsepower of the Leaf. It should have roughly the same performance as the Leaf and 1/4 the energy consumption. If you ran the supercar go-kart and the sedate go-cart on a parallel 0-60 run, the two go-karts would have nearly the same energy consumption. The supercar would have slightly more since it's operating in a slightly less efficient range of the motor, but they'd be close.
In the same way, a Tesla Plaid on a highway onramp just behind a Nissan Leaf is going to use roughly the same amount of power to get up to speed as the Leaf (well, except for differences in curb weight), even though they have the capability to go 0-60 in a couple of seconds. How often do you get to actually go 0-60 in a couple of seconds?