You might be right, if the drianage is poor and the chemical damage not very severe.
However:
>> We first noticed a problem along the fencing of the perimeter of his yard but now the damage seems to be migrating and affecting our cherry tree and other larger bushes. It has also damaged a wisteria vine (I didn't think you could hurt those:)).
His neighbor on the other side of his house is experiencing the same damage.
The trade-off might favor "do whatever you can to get those chemicals moving somewhere ELSE", over "don't drown the roots of already-stressed plants". If the OP has poor drainage, it might be a painful decision.
We have not asked: was that "old fashioned chlorine bleach" (sodium hypochlorite, very nasty) or new-style "oxygen bleach" ?
Even the neighbor might not know!
Looking it up, I see that:
"Liquid oxygen bleach" is actually diluted hydrogen peroxide. (very safe, DON'T add vinegar. No salts, so don't flush.)
"Powdered oxygen bleach" actually has the active ingredients sodium perborate or sodium precarbonate. (??? Salty for sure.)
The I also read that they are said-to-be less toxic and more environmentally safe. I might not always believe that without some substantiation, but in this case, since the alternative is sodium hypochlorite, I'm inclined to believe them.
I assumed that the last-ditch suggestion to add a strong acid to counteract a strong base was based on assuming sodium hypochlorite bleach. But then, the oxidizing agents in "oxygen bleach" are also bases (in the redox sense), so vinegar might affect them also.
Really, I don't know, I'm just extrapolating the suggestion from Daisy's geochemist daughter.
But if the neighbor seems inclined to bleach his patio regularly, I would buy him a big jug of "liquid oxygen bleach" or a small jug of 20% hydrogen peroxide, if that's cheaper.
And bravo to the idea of "flush it onto your OWN yard!!!!!" , excpet that it does seem to diffuse out over time.
Another thing we didn't ask, those who favor flushing the heck out of the abused soil: where it will be flushing TO? Who or what is down-slope?