[rmc]

As a tangent, I hate how trademark law protects the "Amazon" brand for book sellers, but there are 2 different companies. I think that if the company wants to keep a trademark, then any company that uses/is licenced that trademark is legally counted as the same company. This way Joe Soap, upon seeing the "Amazon" trademark, is not able to screwed around by corporate structure shenanigans. Or Amazon Ltd. have the choice of giving up the trademark.

[stickfigure]

I doubt that would matter in this case. Different laws apply to different jurisdictions. The fact that Amazon US and Amazon UK are two different companies is a red herring; a purchase in one jurisdiction may entail different rights than a purchase in other jurisdictions, even from the same company.