technically the energy in green is also not enough to split water, which (IIRC) is why PSII must ping pong the photon through multiple collector complexes to achieve an electron with enough energy to crack water.
The energy required to split water is around 1.25 eV, while the energy of red photons is already around 1.5 V and the energy of green photons is well above 2 eV.
However, it is true that plants need 2 red photons (or of higher energy), not 1, to generate both free oxygen and a reduced organic substance, NADPH, which is used later to reduce carbon dioxide into carbohydrates. The reason is that the captured solar energy is used not only for these redox reactions, but also for pumping ions across the chloroplast membrane. The energy stored in the ion gradient will be used later to power the chemical syntheses, which need both a reducing agent and additional energy.
The ping-pong is done with electrons, not with photons. There are 2 photosystems, which absorb separately photons, using their energy to transport electrons against the potential gradient. The electrons pass through both photosystems in series, achieving a potential difference between the endpoints that is greater than what is required for splitting water.
The potential difference over each photosystem is significantly smaller than corresponding to the energy of the absorbed photon, because only a fraction of the energy is used for electron transport against a potential gradient, while the rest is used for ion transport against a ion concentration gradient.
Photosystem II contains manganese ions that are oxidized so strongly that they can oxidize the oxygen from water, converting it into free dioxygen. Photosystem I is able to make a strong reducing agent, to which the hydrogen remaining from water is bound.
