It’s actually the opposite of what they are trying to claim. Before the free movement of goods in the EU, all goods purchased at the airport were duty free. Since the EU rules, people travelling to non-EU destinations are still eligible for duty free goods, but people travelling within the EU are not.
However, rather than try and have separate shops / prices etc for the 2 different types of customer, there was an agreement made that everyone would get a price that was 'reduced'. The retailers then have to pass on the VAT paid to HMRC for EU travelling customers, but there is no duty to be passed over on the non-EU customers’ purchases. The cost nets off for the retailer....assume the price ex VAT is £1, inc VAT is £1.20 and the retailer sells 1 item to an EU customer and one to a non-EU customer. The retailer gets a total income of £2.20 and passes £0.20 onto HMRC. If, instead the retailer charges everyone £1.10 then the 2 sales still net the same, but there aren't 2 different prices to contend with (but they still have to pass on the VAT on the EU sale at the non 'reduced' price)
In order for them to know which purchases should have duty and which shouldn't they take note of your boarding pass. If you refuse to hand over your boarding pass, they will have to assume that you are an EU travelling customer and pay over the VAT, which, if you were a non-EU travelling customer they would not have had to....thereby potentially costing them money - hence many times they will not serve you if you don't have your boarding pass.
(The reason they would have no issues with water selling water with no boarding pass, is that there is no VAT on water anyway - so no VAT to pay over, and no potential cost).
The set up is no different to a business selling goods to you in person (where they charge VAT) and shipping goods to a US customer, where they would not. They are not making money from the VAT side, it is simply to comply with HMRC / EU VAT regulations.
They are probably making money from the significantly inflated prices that they charge everyone, but that is not a VAT matter.
Sorry for the long post - VAT always gets longwinded!!