My brother is 6'5" and didn't have much of an issue when he sailed with us on the Carnival Sensation. As mentioned the shower heads are mounted on a slide bar so they can be adjusted up and down to best fit your height. He only had to duck slightly, which is better then pretty much anywhere else he showers. The shower head was also a removable hand sprayer so if he wanted he could wash that way, I don't know I didn't ask how he showers.
But I know what your friend is worried about, I have been in old hotels where the shower head was mounted at about 5' which is great to wash out the belly button, not so great to wash the hair (I'm also 6').