quantum mechanics - Does a photon interfere only with itself?

I sometimes hear statements like:

Quantum-mechanically, an interference pattern occurs due to quantum interference of the wavefunction of a photon. The wavefunction of a single photon only interferes with itself. Different photons (for example from different atoms) do not interfere.

First of all -- is this correct?

If it is correct -- how do we explain basic classical interference, when we don't care about where the plane waves came from?

I heard that there are experiments with interference of two different lasers -- is this considered as a refutation of the statement? If it is -- how should one formally describe such a process of interference of different photons?

Finally -- such statements are usually attributed to Dirac. Did Dirac really say something like that?