...I believe it's an old brewers' myth, myself.
Could be. Or, it cold be a problem only in theory
All I know is that the late and lamented Vernon Valley Brewery (NJ's first, pioneering Microbrewery in the mid 1980s) made the
best authentic German beer this side of the Atlantic. A friend of mine (the late Jay Misson) was a brewmaster there and he told me that they cooled their wort by cascading it over a heat exchanger.
They seemed not to worry about HSA at all, and from what I tasted (draught and bottled), there was zero
effect on the beer in the short term or
the long term.
Ever since then, I never gave HSA a second thought.