...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.
If I find a shiny rock and sell it to you for $100 and you find a fossil and sell it to me for $100, that's $200 added to the GDP. If we trade rather than pay each other, then it's $0 added to GDP. The same goes for services. If I mow your lawn, paint your house, hypnotize you to quit smoking, or sing you a song - all of those things (are included in GDP.
When you pay for entertainment it's 100% included in GDP the same way as when you pay for somebody to inspect your car.
The other comment had it right though - taxes would kill this scheme.