I’m another poster that hasn’t listened to the programme in the OP (sorry) but I’m pretty certain I know the research to which it’s referring. It stands to reason: electric motors are very efficient at converting stored energy to motion. Even when you go back several steps and consider the generation/distribution and battery charge/discharge losses, they’re still pretty good. The human body is much less efficient at converting stored energy (i.e. food) to motion (I’m sure there’s a number in the programme, but from memory, about 25-30% is the ballpark), especially when you start to consider the environmental effects of producing that food.
The big flaw is that there are so many variables, as has been pointed out already: how the electricity for the e-bike is generated, distributed, and stored, will change a lot, but the variation depending on the human diet and physiology is massive.
The other thing is: we need exercise to maintain our health, so if you sit on an e-bike expending no energy*, and then have to go to the gym to exercise at a different time, it’s not exactly a gain is it?
*I’m assuming an “electric motorbike”, not a pedelec, for simplicity, before the pendants arrive.