Wireless power transfer - Inductive vs. resonant mode
In most inductive coupling products, the primary and the secondary are both tuned. When the two tuned circuits physically come-together they detune each other: -



When coupling is small (k &lt; 0.01) there is quite a tight central peak (about 10 MHz) but as coupling gets larger, the central peak splits into two peaks that start to move away from each other as coupling improves so, you could choose to drive the primary at a slightly lower or a slightly higher frequency than 10 MHz and get an improvement in coupling. Clearly as coupling approaches 0.1 the peaks are quite seperate so this technique sounds like a good idea.


  They claim that when the units are in very close proximity it is more
  efficient to oscillate at the inductive side of the resonance
  frequency, but when further apart it is better to ride on top of the
  resonance peak.


As far as I can tell it will work on either side of resonance. See this answer that shows the same happens with capacitively coupled tuned circuits.