I wouldn't say that is completely true. It would depend on the heads being switched between. Plenty of heads are exactly the same, except for the hair or earrings, etc. Switching between two heads that are that similar could be easily explained as accessorizing or putting a pin in your hair.
Assuming that is what the OP was after and not something to change to a completely different head, it wouldn't be breaking to gameplay. Though, somewhat related, the tattoo artists being able to change tattoo color might be an outdated feature for our server. Many of our newer heads use tattoo color to determine the eye color. Being able to change
that is a more reliable way to avoid IC recognition than any simple hair scrunchy would be.
Edit:
Examples -Human Male
102,
141, Human Female
160,
161