Of course they pay the VAT to HMRC. They collect the VAT, since it's paid to the company when you buy something off of them - customers don't make a separate payment to the government every time they make a purchase! But the essential point is that every penny of the VAT from their sales comes direct from a customer.
Unlike income tax and employees, customers are not legally liable for VAT on goods they buy, rather companies are liable for VAT on what they sell. So it's not just a question of accounting and collection. VAT is a tax paid by the company.
Of course ultimately the costs fall on the customer as do all costs. Would you say that RPi doesn't pay for components because the customer ultimately pays for these too?
The original post said that RPi paid no tax which is without doubt factually incorrect.
