One can have a "whippy" bike that is constantly out of sync with its rider and a rubber noodle of a thing (done that). A "stiff" bike can plane or be in sync with its rider. It can also be rubbish (done that, too!). 1983 Specialized Expedition (3500g frame/fork/headset, 63.5cm CTT size) "planed" with me at speeds as low as 7 mph, and it was not some soggy thing. Incredibly rapid and free-flowing at speeds above that. Epic frame/bike (this is with decent/nice 700C wheels and tires--no boat anchor components need apply). 1981 Trek 716 (65.5cm size) was whippy, and amenable to out-of-saddle efforts. Planing wasn't really a thing, but we got along well.

I think, for someone to come to a conclusion that a bike really planes, that rider must decently explore the performance envelope of said frame/bike. Not some foolish kamikaze downhill effort, but certainly out-of-saddle efforts in conjunction with the rider's size/weight and strength (aka ability to ascertain). I am of the mindset that a bike can plane while in the saddle, as well as feel at least a little whippy, but unless the frame is given enterprising wheels and tires, in combination with harder (out of saddle) effort, full context is never realized, and thus a complete explanation is curtailed.
[MENTION=506308]ctak[/MENTION] 's 700 series is likely a lot like my 716, but focused a little more due to 24" (61cm-ish) size and tidier chain stays. Focused flow, especially with aero wheels and supple tires (to say nothing of his general fitness, endurance, and ability to probe the capabilities of said frame/bike).