The claims are utter garbage. Some are claiming 70 or 80NM, as much as some small cars produce. That's clearly guff. Tow a small car with a bicycle chain using sufficient torque to get it moving and its doubtful the chain would survive, which just shows how preposterous the effort and power claims are.
A bit iffy as an unqualified claim, but not necessarily a lie. It's quite possible that a 250W rated bike motor could produce the same torque at its crankshaft as a small car. The missing bit of the equation is rpm.
kW = 0.105 x Nm x rpm / 1000. So your small car with 80Nm @ 5000 rpm will produce 42kW, about 56bhp. Your 80Nm bike, at a cadence of 60, would produce 0.5kW or 500W, which is just about credible as a peak power figure for a motor with a continuous power rating of 250W.
Watts = Amps * Volts so at 36V, you'd need 14A to produce half a kW. That also sounds credible - 15A - 20A controllers wouldn't be unusual, would they?
If the pedaller was only maintaining a cadence of 30, then 80Nm would produce c. 250W, the rating of the motor. What they don't quote (there is as you say no standard) is the rpm at which peak torque is produced.
I don't entirely disagree with your drift because there will undoubtedly be conditions in which the motor can't add 300% - because the rpm are too low perhaps, or the rider input is very high. But 40-80 Nm is quite on the cards at the cranks.
EDIT - you can do similar sums for a person. It's said that a fit cyclist can produce around 250W. If he or she is doing that at a cadence of 60, then they are applying torque of about 40Nm. To deliver 250W at a cadence of 30 would require the magic 80Nm.
I think it's reasonable to claim that an e-bike typically applies significantly more torque (force) to the drive train than an average Sunday cyclist. Inexperienced cyclists are probably the worst for the drive train because they tend to use low cadence (therefor more torque for the same power).
P.P.S. - 10 Newtons is equivalent to 1 Kilogram force. I Don't know how much you weigh, but if you can apply 50Kg. of your weight to a 170mm crank at the horizontal then at that moment you are applying about >80 Nm. to the crank yourself - 500 Newtons at 0.17 metres being 500 x 0.17 = 85Nm. Of course, if the crank was stationary you would be producing 85Nm. but no power at all.
