You are saying that one water molecule loses its oxygen atom and replaces it with a (normally identical) oxygen atom from the CO2 molecule, while the other loses its oxygen atom then combines with the remaining CO from the CO2 molecule to become part of a carbohydrate, thus the O2 comes from the water.
I am saying that the final result of the reaction is that one water molecule is still a water molecule, the other gets combined with the carbon atom from the CO2 molecule to form part of a carbohydrate, and an O2 molecule replaces the CO2 molecule from the air.
One could argue that half of the released oxygen comes from water, while the CO2 retains one of its oxygen atoms, but you can't argue that the other water molecule contributes anything, since the oxygen atom it gives up is replaced with another (to no net effect, unless you care whether it's O14 or O16.
Did you bother to read rhe text?
That discovery received an award; science is the business of certainty, not odds.