Why wouldn't it be influenced? Think about a binary star system. Replace one of the stars with a black hole and nothing is really different. I'm not sure how you could say that it wouldn't be influenced by the presence of another object...
The light - well the light that would otherwise be emitted if the star weren't of sufficient mass to have it's event horizon be outside of it's physical outer boundary. The "it" that I referred to in "stretching it into an oval shape" is really the event horizon of the black hole.
I'm one of those that doesn't believe in the singularity aspect of a black hole. I think a black hole is just a star that has sufficient mass and density such that it's event horizon is beyond it's exterior. I don't think anything magical happens inside, I think it's just a regular star, or a neutron star. Even there were a singularity, my idea about pulsars isn't really any different.
The idea is simply that, the gravity field of a single star, black hole, or planet if it has no neighbors is spherical. If it's in a tight orbit with another body, as is with a binary star system, then it's gravitational field could be considered elliptical (if you imagine removing the other body - like take the moon out of the picture and just think about the earth's gravity field - it would be eliptical). I'm making the jump that the event horizon of a black hole in a binary system would also be elliptical. If that gravity field IS elliptical, then it's possible that radiation (I called it light) could escape at the edges.