Wouldn't somebody somewhere in this kind of transaction have to pay the VAT, thus rendering this impossible?
People indulge a lot of strange and wrong ideas about economics and, not surprisingly, those bad ideas are typically well aligned with their preferred world views.
The other comment had it right though - taxes would kill this scheme.
...with no more veracity than your hypothetical. You don't understand what GDP measures. You've allowed yourself to believe that the economists involved are naive. You are correct, however, that this sort of bad thinking is common. Very common.
When you pay for entertainment it's 100% included in GDP the same way as when you pay for somebody to inspect your car.