can anyone do the actual math to prove this?

I can do some math that I believe disproves it. Say there's one fluid ounce of headspace per bottle, so roughly 50 fl oz (1500 mL) total, versus maybe 500 mL (one pint) of headspace in a keg. Once fermentation is finished and the dissolved CO2 reaches equilibrium, the head pressure (at room temperature) is going to be roughly 30 psig, or ~3 atm absolute.

The additional CO2 required to prime the bottles' headspace is 1 L * 2 g/L * 3 atm = 6 g.

The additional sugar required to produce that 6 g CO2 is about 13 g (0.45 oz).