Out of curiosity, what does shampooing your hair have to do with going to the gym? Is this the only time you ever get out of the house?
I think he is implying there isn't any physical exertion on non-gym days, thus no sweating. Likely has a white collar job, and thus nothing environmental really making his hair nasty.
I have short hair too, and if I haven't really done anything, I make it a point not to shower that day. It dries my hair out and my scalp.
Hell I'll even admit I don't shower on days I don't do much. After showing, it's either I have to apply lotion (specifically on my face) or wait half a day for the natural oils to start doing their job. And I cannot wash my face unless by washing that means standing under the shower head, essentially rinsing my face. Otherwise super dry face (water alone dries the skin enough).
I'd rather have some natural oil on my skin that have completely barren skin. Especially in the winter where it just never gets to the point of moisturizing itself.
In the summer, or warm environments in general, things are different. Sweat and oil, on both skin and scalp, need daily cleansing unless I didn't even leave the house.
Unless the environment dictates otherwise, showering daily is generally a bad idea. It's a good wake up call, but our body kind of relies on what it builds up, and for some reason our society enjoys the spoils of excess in terms of grooming.
I for one would rather skip a day than have super dry skin and either go the day with flaky skin on my face and scalp, or require oily products to be used right after the shower...