It's not that I don't believe this may well be true under lab conditions, or that many fish in the wild can tolerate quick changes in water chemistry without undue harm. But I think it's a misleading factoid when used in fishkeeping.
For a start, fish adapted to high pH levels quite clearly have little to no tolerance of acidic water. Try changing the pH of a Malawi, Tanganyikan, brackish water or marine aquarium from 8 to 6 and you'll get a lot of dead fish whether you do it quickly or slowly! Conversely, fish adapted to very soft water habitats such as rams, wild discus and Hemirhamphodon halfbeaks are used to water that contains few bacteria; keep them in hard water tanks with a high pH and they're much more prone to infections. Other pH-related issues include the toxicity of ammonia and nitrite at varying pH levels, and the decreasing effectiveness of biological filtration at acidic pH levels.
So there are plenty of practical reasons why a particular pH will be optimal for a given aquarium.
The key thing is that pH, hardness and carbonate hardness all go together. Too many aquarists focus on just one thing, usually pH, without understanding that the other two aspects of water chemistry need to be considered and perhaps altered accordingly. Hence my argument that if you don't understand all three aspects, don't change any of them; and if you're going to change one of them, then you will probably need to adjust or at least monitor the others too.
Cheers, Neale