The Foundation may (probably does, but no one knows for certain) not pay taxes, because of its charitable status. I'd be very surprised if the Swiss SAs don't, given corporate income tax is levied at federal, cantonal and communal level, unless they are all unprofitable, which seems unlikely.
Legally, of course you are correct that the UK company is a separate entity, so it's not simply a big difference, it's an absolute difference in those terms.
However, the UK company is a wholly owned subsidiary, and in practical terms, that is £10 million less funneling back to Geneva. Any statement that states that Rolex pays no taxes depends on a conception of Rolex as solely the Foundation. No doubt some other members of the Rolex Group also pay corporate income taxes in their respective countries of incorporation.
That's before you consider sales taxes (which I don't think it fair to include, as in England VAT is paid by the consumer, not the company, although the company collects the tax on behalf of HMRC). However, I see that Switzerland also has employer taxes, and I assume that the Rolex entities incorporated in Switzerland have employees. So it is probably fair to infer that Rolex at least pays employer taxes in Switzerland.
Whilst disappearing down this rabbit hole, on a slightly different subject, it was interesting to note how little stock the UK company carries compared to its turnover. I suppose not surprising when you think about it.
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