Your HMRC friend is a it misleading. He is correct to say if EU countries insisting on you paying THEIR vat that would be money grabbing. But he omitted to say that the way most EU traders sell to consumers in the UK is they charge the UK VAT on goods at the point of sale if below £135 or E150 and then forward the VAT to the UK government. This is the UK process. If they fail to do that, then the courier will come knocking on your door for the tax and vat and get the EU exporter a bad reputation. The same happens in reveres for UK exports.
@JohnPW is correct in how it operates.
Above £135 there is import duty to pay as well as VAT, this should be collected at point of delivery, which is why a lot of retailers have temporarily stopped exporting to the UK as retail customers are not used to paying tax to the delivery courier /postman. For this reason most UK exporters are having to set up distribution centres in the EU and vice versa or make an arrangement with a 3rd party to handle the import and export duties so that the consumer does not feel the pain.
Most of us have run into this when buy form Amazon of ebay form US companies and then found they had to pay import tax at the customs depot in the past. Although its less of an issue now as US retailers have started to apply these charges up front.
Many Chinese traders got round these rules by disappearing and prearranging under a new trading name to keep one step ahead of HMRC. The latest round of this cat and mouse game saw HMCR require Amazon and ebay to apply 20% vat on all imports and collect the tax on HMRC's behalf which is why prices rose 20% in January. I've noticed that prices are coming down again so I guess the mice have found another way to avoid paying the import duty /vat.
Its quite involeved and confusing for us consumers.