Q.Why Do You Write That Purple Leaves Are A Sign Of Disease?
In a hydrangea serrata, it is not at all a sign of disease. Many serrata, such as Blue Billow, are known for their purple fall leaves. You show a hydrangea serrata in your photo illustrating what you are calling a disease https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-leaves-turn-purple.htm

Certified GKH Gardening Expert
As long as this is in Autumn, and you know that your cultivar has the tendency to undergo senescence, then you can ignore this rule. For ANY other cultivar in any other season, this will be a sign of phosphorous deficiency, pH swings, or other distressing conditions. This can be confirmed with a soil test, or pH test.

I concur with you. It is common for hydrangea foliage to turn purple, albeit not during the whole growing season. But note that this is not limited to serratas. For example, macrophyllas, serratas and quercifolias can show purple colors too. Not all varieties may do so. And the ones that do, may not do so everywhere.
At the start of the growing season, early frost damage can cause a series of unusual foliage colors that include purples, redd/oranges/etc. At the end of the growing season, fall foliage can sometimes turn purple, red/orange, yellow, and several shades of brown.
But a purple color that lasts for long periods of time should be researched to see if it is a phosphorus deficiency.
In the article, I would suggest displaying several pictures of purple foliage with comments below that identify it as being normal for fall, phosphorus deficiency or cercospora leaf spot. The picture in the article is not that of cercospora leaf spot.