Well the tires where new, so that wasn't the problem, bearings where good too, no play in them. Rear suspension though might have been a likely culprit. There was also some rust issues around the sidestand area we discovered when we tore apart the bike so that might have weakened the frame and perhaps induces some frame flex?
Interesting what you say about the rusty frame, because that might be what it is... read on.
One thing that caught me out recently was the very slow wear rate and gradual decline of the swingarm bearings. A weird handling problem that gradually got worse over a few months. Nothing major, just a slight step-like uncertainty, that felt for all the world like tyres that were old and unsuitable (yes, they were) but that wasn't actually the problem. It had been so long since I last had to adjust the s/a bearings, I'd forgotten what it felt like. The actual adjustment needed was in the order of about 1/12th of a turn - just enough to remove the slightest degree of play I could only just feel in the arm.
A frame that is weak in that area, because of rust or damage, might lead to some uncertain handling.