Like Pierre Castille above said;
It's the resonance!
Small birds and bats, and all flying insects beat their wings at a rate that resonates to their wings physiognomy. There is a push on the thrust producing down stroke, most of the rest of the motion is produced by elasticity in the tendons (and exoskeleton for insects).
So, once in flight, it takes a periodic pulse of muscle to maintain the harmonic motion of the wing stroke, unlike a rotary propeller, which needs a constant applied motion to maintain lift.
(Stupid analogy time: Compare the amount of energy needed to bounce a ball rapidly, with the amount needed to hold the ball and carry it up and down with muscle power the same distance and speed.)
Really, the good Doctor sounds like the Victorian scientists that maintained that bees were too heavy to fly, and dogs were only overheating themselves more by panting. We've learned a bit since then.
(Seriously, a pigeon attempting to fly with a load it isn't designed to carry is less efficient than an aircraft carrying a load it's designed for? To quote Paula Bean http://thedailywtf.com/Articles/The_Brillant_Paula_Bean.aspx , "Brillant!")
I chose the penguin, it's rather inefficient at flight too.