I doubt Apple or Amazon is specifying how the LEDs are made. This is a weirdness in patent law, in that you can sue the user of patent infringing part, not the manufacturer.
This is not an entirely weird idea. Specifically, if your design incorporates a CDMA part, you will have to pay a patent royalty on the use of CDMA to Qualcomm of $35. The catch is that the royalty is only due on the part if you import it into the U.S. where there is a patent in effect on CDMA, and not due in other markets where there is not a CDMA patent in effect.
So BU may have some standing here, if the off the shelf parts using their technology did not have a license from BU to use the patented technology in the manufacture of those parts; if that's the case, then a royalty must be negotiated for importation of the device manufactured in an area with no patent on the technology into a market where such a patent applies.
This is something of a dirty trick, since often the patent holders will engage in selective enforcement against people with deep pockets. I.e. you can buy the same part yourself from Digikey or other vendors, or from Chinese and Japanese vendors, and have it drop-shipped to you in the U.S., or even have devices built abroad using the part and import it into the U.S., and BU will likely not sue you until you have deep pockets.
One of the failings of patent law is that, unlike trademarks, which have to be rigorously defended for them to remain in force, patents do not require rigorous defense. Likewise, while attempting to treat IP (Intellectual Property) as real property for enforcement purposes, the courts do not recognize the doctrine of adverse use/adverse possession, in which, after a period, if not stopped from use, the user establishes an interest and therefore the owner can not contest it. It's rather like being able to "have your cake and eat it too".
Hopefully there will be some patent reform soon; meanwhile, yes, BU is playing a dirty trick by not going after "first offender first", but they are likely within their rights... ...assuming of course the first principle that the off the shelf parts used in the devices were not manufactured under license of the patent from BU. If that assumption is invalid, then BU is just trolling for a settlement and shouldn't be allowed to get away with it.