It's no wonder that there is much confusion about ionized water these days. Doing a Google search leads to this Wikipedia article where it says "A water ionizer (also known as a alkaline ionizer) is a home appliance which claims to raise the pH of drinking water by using electrolysis to separate the incoming water stream into acidic and alkaline components."
Already in the first paragraph the article shows a strong bias. To me, this article is absolutely ridiculous. There's no doubt that a water ionizer alters the pH level. A simple pH test from any garden store will prove that the pH level is different.