My goodness, there's some wool-pulling going on here
All these arguments about power, HR and cadence are missing the essential physiological understanding of how a human body works.
Consider moving a load at slow speed - analogous to low cadence. For a given output (power, if you like), the main force-producing muscles are dominant in both result and energy use over the muscles which control the stability of the working limb(s). For a cyclist, this means that, until you get to 'hauling on the handlebar' levels of leverage, lower cadences require a smaller proportion of input from stabilising muscles. With increasing cadence, for the same output, the effort required from the main propulsion muscles is smaller but the stabilising muscles are increasingly required to off set the tendency of the limbs to lose alignment, hips to sway, shoulders to rock etc. At very high cadences with low resistance - typical for spinning class intervals - the stabilising muscles are the major energy-consuming part of the system since the effort required from the propulsion muscles is vastly reduced.
Since the measured (power) output is the same for the different cadences in your example, you've been making the assumption that the body is making the same exertion to achieve it - clearly this isn't the case, as Jimbo's initial experiment shows.
Training is used to improve the efficiency of the stabilising muscles (also called postural system as it's basically responsible for keeping us upright) - typically they're weak relative to propulsion muscles. People who are more anatomically 'perfect' (better joint alignment, less stiff hamstrings and other muscles etc.) will usually find high cadences easier than those who have muscular and joint imbalances as the demands on the postural system are smaller.
This explains why HR isn't simply correlated with power output (so a set of valid ramp tests for comparison over a training period requires a test protocol so that power output is achieved using the same gearing/cadence in each test), nor calorie expenditure with power, as you're missing a component which is variable with cadence.
BTW The importance of the postural system in sports has only been recognised in the last 20 years or so as intense training to develop propulsion muscles can lead to parts of the postural system being rendered 'redundant' - which leads to instabilities developing. Shoulder injuries in swimmers were a good example as the over development of the big muscles like traps/pecs for propulsion lead to the smaller muscles, which control shoulder alignment through the complex 3-D movements, becoming ineffective. The exercises required to correct this are small precise movements (think Pilates) to target the individual postural muscles and strengthen them. Often cyclists' knee problems are of a similar origin with marked but unbalanced development of the quads.
Lecture over