Photosynthesis A2 help

So I've been looking through the photosynthesis part of my textbook. In reference to non-cyclic photophosphorylation it says that electrons from photosystem I are joined to NADP to produce reduced NADP. All good. then a bit further down it says that the protons produced from photolysis of water are used to reduce NADP.
So NADP can be reduced by protons or electrons? How does that make sense?

It's a similar issue in respiration, NAD accepts hydrogen in glycolysis, making it into reduced NAD. But according to everything I've learned in chemistry, reduction is the gain of ELECTRONS, not freaking protons?!

Anyway, please help if you have a clue

A compound may be reduced by the addition of electrons, by the addition of hydrogen/protons, or by the removal of oxygen. Likewise, a compound may be oxidised by the removal of electrons, the removal of protons/hydrogen, or by the addition of oxygen. It is hard when you've had OILRIG drummed into you since GCSE and no-one has introduced you to a wider definition of reduction and oxidation.

This webpage is good, if you want a better explanation of the different definitions:
http://www.chemguide.co.uk/inorganic/redox/definitions.html