I wonder if this story is true. These are different kinds of alcohol, and most people know the difference. I am sure that most Muslims routinely use products that contain the non-consumable forms of alcohol.
I have several “moderate” Muslim dental patients who use mouthwashes that contain alcohol. They say alcohol is not forbidden if it is for medicinal purposes. But I also have some who won’t touch alcohol in any form. I know people who have traveled to the Middle East and had their Listerine confiscated. Muslim medical facilities and hospitals use peroxide products for disinfection, from what I’ve been told.