I think you may need to re-examine your definition of evidence.
Is HSA a big, terrible risk if you so much as breathe near your wort?
No.
Is there very well documented evidence that hot wort agitation will contribute to the development/acceleration of chemical pathways involved in staling?
Yes.
In most circumstances, unless you are whisking as you suggest, or possibly pumping/whirlpooling hot and for 20 or so mins - it may not be. Certainly running that whirlpool cooler is as much insurance as using hose rather than splashing straight from the tap or pouring.
The mechanisms that lead to staling are not completely understood and HSA is only one tiny piece of a puzzle that may be of no concern (as suggested in my initial post). However if you have noticeable issues (as mtb has recently suggested he does) it MAY be a contributing factor.
Unicorns on the other hand......
Unlikely to be a problem in most circumstances is different to entirely imaginary.