The principle of non-locality states *"that an object is influenced directly only by its immediate surroundings."* [(Wikipedia)](http://en.wikipedia.org/wiki/Principle_of_locality)

![enter image description here](https://i.stack.imgur.com/UO6OG.jpg)

When two entangled particles are measured in an EPR experiment, we consider these events as **non-local**. Generally I agree. But does this also apply to a pair of **photons in vacuum**? (and if so, why?) 

![enter image description here](https://i.stack.imgur.com/t7lDE.jpg)
From the point of view of any observer's Minkowski diagram, the two spacetime intervals of the lightlike worldlines of the two photons AB and AC are always zero (so-called "empty intervals"), and by consequence, B and C are located in the "immediate surroundings" of A, and the events should not be nonlocal. 

For more clarity I replaced "B in immediate surroundings of C" by "B&C in the immediate surroundings of A". In spite of the attribution of a bounty, the question is still unanswered.

As user 12262 pointed out, some comments have disappeared in the meanwhile.

Edit 01/07/14: Up to now, no answer explains why there is the word "interval" in "spacetime interval = 0".