The StackExchange post that he linked lists several cases where it's possible. I was skeptical too - I was a physics major in college, I know all about potential vs. kinetic energy and rolling resistance. But engines are not perfectly efficient: you're going to lose some energy to internal friction within the engine, and to combustion efficiency, and to transmission losses, and to a number of other effects which vary based on speed, RPM, and torque. Add in an engine computer that's trying to minimize these effects based on inputs, and actual fuel efficiency will vary significantly from the simple "chemical energy in = kinetic energy out" model.
I've also observed the effect that the OP mentioned: in my Honda Fit, I get a fairly consistent ~45 MPG on 101 (completely flat highway terrain), ~40 MPG on 280 (rolling hills, highway), and ~43 MPG on 84 (across the Santa Cruz Mountains; ascends 3000 ft. in a series of tight switchbacks and then descends 3000 ft. in a wavy line). My working hypothesis is that the descent on 84 is consistent enough that the engine computer can idle the engine for all of it, burning no fuel - this is consistent with the car being nearly silent on the downhill, and of the instantaneous mileage display being stuck at its max of 80 MPG. Probably also helps that speeds are much lower, so there's less air resistance.
Anyway, the point is that cars are complex enough that the simple models you learn in Physics 101 don't really hold.
Engines are most efficient at WOT. Hilly ascents at WOT will burn the fuel more efficiently (even though you're using more). Add a descent in which the computer stops providing fuel and it's possible that you could get a better mileage.
It's known that you can get better fuel economy by oscillating speed on flat ground - using WOT to gain speed, coasting back down, opening up WOT again. This is because the engine is most efficient under load and the average consumption works out better. Adding in the hills would average this effect.
Generally not wide open throttle - see the efficiency maps I linked to in another reply. Generally peak is at somewhere around 1/2 to 2/3rds maximum output.
Wide open throttle and percentage of maximum output are two different concepts. An engine operating at partial throttle has higher pumping losses (pulling air past the partially closed throttle plates).
An engine operating at WOT but still producing a fraction of its maximum output is certainly possible (and generally more efficient than an engine producing the same output at a partial throttle setting). A diesel engine is almost always in this configuration (metering fuel but generally not restricting air with a throttle plate) and a gas engine at low RPM but WOT is also in this state.
If tuned for efficiency in that config, it can be very efficient and is how many piston airplane engines are regularly operated where fuel consumption is an important part of range (and operating economics).
I've also observed the effect that the OP mentioned: in my Honda Fit, I get a fairly consistent ~45 MPG on 101 (completely flat highway terrain), ~40 MPG on 280 (rolling hills, highway), and ~43 MPG on 84 (across the Santa Cruz Mountains; ascends 3000 ft. in a series of tight switchbacks and then descends 3000 ft. in a wavy line). My working hypothesis is that the descent on 84 is consistent enough that the engine computer can idle the engine for all of it, burning no fuel - this is consistent with the car being nearly silent on the downhill, and of the instantaneous mileage display being stuck at its max of 80 MPG. Probably also helps that speeds are much lower, so there's less air resistance.
Anyway, the point is that cars are complex enough that the simple models you learn in Physics 101 don't really hold.