Sunday afternoon, too hungover to lfg... So I analyzed the 1000000 RNG-numbers kindly made available from Christer.

Here the results of my little program:
Read 1000000 Rolls amounting to: 3500887.0
Number of 1's = 166591. average chance: 0.166591
Number of 2's = 166894. average chance: 0.166894
Number of 3's = 166498. average chance: 0.166498
Number of 4's = 166298. average chance: 0.166298
Number of 5's = 166492. average chance: 0.166492
Number of 6's = 167227. average chance: 0.167227
Average roll: 3.500887


there were 333 more sixes rolled than the next higher numbers of rolls (2), which probably is the cause for the slightly higher average roll (3.5 would be the mathematically correct average)

q.e.d.

Edit: thanks to rudinho for pointing out that there are 8 same number streaks for 6,5,4 and 2.


Edit2: This whole exercise was completely useless, as it doesn't prove any randomness of the numbers ;)