That’s right, for businesses that are able to claim VAT, there’s no overall cost. The calculated VAT amounts are recorded in both box 1 and box 4 of the VAT return. I’ve never used Sage but I’m guessing that perhaps that tax code calculates and records the amounts.
For businesses that aren’t able to reclaim VAT, there will be a cost – although they would have had the same cost if they had been able to buy the service from a UK based supplier.