The way manufacturers have been claiming it is by under rating the 8R and 4R figures to give the illusion audiophiles want to buy into.
I think you've hit the nail on the head with this comment. The audiophile press seems to have convinced many of their readers that if your amp doesn't double power as impedance halves you're missing something in sound quality. Something audible. For most listening levels in most rooms with most material, even action movies, you're very unlikely to miss anything SQ-wise if your amp has relatively high power (e.g. ~200W/ch into 8 ohms) and only delivers 50% more power into 4 ohms than 8 ohms.
I know there are some speakers that have been tested that have very low impedance into some important frequency ranges (the Legacy Focus Stereophile tested comes to mind), but these are exceptions. The old Apogee Scintillas also come to mind. But most speakers do not have impedance curves that fall substantially below 4 ohms. These two examples are exceptions.
I think power doubling is mostly an audiophile press driven requirement that isn't supported by the facts.