This is a constant subject among individuals who took psychedelics.

We don't have the comprehension of brain, mind and conscioussness yet to really defend telepathy. But we can do tests to check if it is real, and I would guess it would fail miserably.

I would guess it is more an impression than a real fact, but maybe under the influence of psychedelics you are more opened to external stimulae (if you can perceive the external world), thus making your perception more accurate and also you can "read" the situation in a different perspective.

I myself had perceived many familiar places as dirty (also a common thing among psychedelic users) because you denaturalize your way of view things, plus you can perceive better the details so you can now see what was always there but your brain chose to ignore (the brain-filter hypothesis from Huxley in Doors of Perception). I think the same apply to "telepathy": you denaturalize your image of the other person (like the way you already had perceive their personality, identity etc) and you are more opened to details, thus you can antecipate (in a limited level) the feelings and thoughts of a person like a competent psychologist would do. Since you both are sharing a similar experience, I can totally see a perception of telepathy in this kind of situation.

It really is very interesting that such a specific paranormal ability is perceived by so many people. Further investigation is required.