Having played the game for several days now I must confess that my initial enthusiasm for them sticking to the rules of the tabletop have diminished.
Spoiler:
The game neither cheats, nor is there anything wrong with the randomness. What you're seeing is the method by which the game prevents cheating in multiplayer games and allows for easy reproduction of the game in replay files.
What you first have to understand is that "random" on computers is done via a complex mathematical formula applied to a number called the "seed". If you seed a random number generator with the same number twice, then ask for 6 random numbers... you'll get the SAME six random numbers in the same order. This is still random, and the distribution over time will bear out its randomness, its just how computers work.
Blood Bowl sets and stores the seed for a given game at the start of that game. In multiplayer that means that even if the other player went in with a memory editor and changed his rolls to 6, you'd know immediately because your computer can verify that 6 is not what he was meant to roll based on the shared RNG seed. Its a fairly common method to prevent cheating in P2P games requiring randomness.
Likewise, it means the game replays can reproduce the original game state without actually storing any dice rolls - it can accurately re-create those dice rolls by simply having the original seed, and knowing what actions you took during the game.
One thing for sure, if u want to play this game with so much fun, u need to learn the rules FIRST !
This game is designed for its fans so new casual gamer absolutely need to learn the basic rules first & do some tutorial or one match first to try something in this game...