Regardless of the video being incorrect, it is obviously possible for stars to collide, a fact we believe we already have evidence of happening recently (in stellar terms) in a nearby galaxy, as the supernova detected earlier in the year appears to suggest that a star that normally wouldn't have the mass to supernova has actually gone supernova, and contains elements that we currently believe can only be formed by the collision of two stars.
However, a collision like this happening in any one galaxy is pretty rare - even amoungst a cluster of galaxies it likely only happens only a few times every 100 years - so it isn't really something you would expect to witness in Elite, and you obviously wouldn't want to be near it if it did.
Collisions are more likely to be avoided and instead the stars are more likely to begin orbiting each other, quite possibly explaining the high frequency of multi-star systems.
