See, this sounds insane at face value, until you remember that Louis Pasteur had only invented pasteurization in 1865, that Robert Koch published his postulates on the link between microorganisms and diseases in 1884 (after this book was published), and that Dr John Snow's research on the Broad Street cholera outbreak of 1854 (in which he proved that cholera was waterborne and not caused by bad smells, as the entire medical establishment believed) was not publically accepted until 1866, eight years after his death (and only 16 years before this book was published) -- and despite that, there were still people who doggedly insisted on believing in miasma theory (aka that disease is caused by "bad air" or bad smells) well beyond that.
So the writer of this book isn't actually.... wrong, per se. In an age before they had clean, sanitary, safe drinking water, you probably DID get at MINIMUM awful diarrhea pretty regularly after drinking water. This is why so many people drank small-beer (very low alcohol content, but the fermentation process (and by some preparations, boiling the water) killed the dangerous microbes and made it safe to drink). The popularization of tea actually really cut down on cholera outbreaks and other water-related digestive troubles as well! not only because you have to boil the water, but the tannins in tea also kill off (at least some) bacteria.
And in case you cannot comprehend the state of how breathtakingly "they didn't fucking know" -- If you were really poor in London in the first half of the 19th century, you were often literally dipping a bucket into the nearest gutter, letting it sit for a day for the solids to separate out, and drinking what was left. Even the well-to-do houses with fancy newfangled running water were at risk of waterborne illnesses, because a lot of those water supply companies had intake pipes stuck into the fucking Thames (you know. the famously polluted river that all the sewers dumped into) and were so negligent about filtering it that people sometimes got live eels coming out of their faucets.
So yeah, drinking many glasses of water IS a potentially injurious one and DOES weaken digestive power -- IF you are unfortunate enough to live in the 19th century before public health became a government concern.
(I just read a book on the Broad Street cholera outbreak yesterday, The Ghost Map, and it was riveting, highly recommend -- the Broad Street pump's well, which provided water to thousands of people in a neighborhood of London, was situated two and a half feet away from a cesspit where residents of a house were dumping their sewage. According to reports by the inspectors after the fact, the bricks lining the cesspit were so degraded that they could be removed with hands, and upon excavation, the earth between the cesspit and the well was muddy and saturated with human waste. The well's water level was eight feet below that of the cesspit.)