The System.Random is just not very good, you should not use it if you need something fast or cryptographically secure... But as a first choice for just a few random numbers it's good enough and it was chosen specifically for its capability to split a generator into two, so that's probably what you should be using if you're going to do simulations in parallel with System.Random. Or use random seeds at least !
This is specifically an interaction between random*R* and mkStdGen with low seeds (random don't seem to have this particular flaw), since we're still using a pseudo-random generator, we ought to be pretty careful in the way we use it (those have always been touchy beasts) and this particular usage seems to be a bad counter-example of what to do with a PRNG.