I'm going to move on to the next part now, and that's how, potentially, refs can influence a game. I wish I had more time up my sleeve to watch some replays and observe if these things actually go on as often (and as accurately) as I recall from watching live, but let's look at it in theory.
To influence momentum in a game, there are two main avenues - penalties and marking the 10 metre defensive line. Penalties are an easy one to explain. Simply look for easy excuses to blow the whistle. You'd be hard presses to catch a ruck that doesn't have some kind of infringement, an unfortunate side-effect of "letting the game flow". So finding a slow defender, hand on the ball, etc, is easy.
I think the 10 metres is just as important though, and is one aspect that is very rarely scrutinised. It also influences the game more in terms of momentum with the ball-in-hand, not just field position. For starters, most tackles & rucks don't just stop at a certain point that the 10 can be ruled off. Everyone is struggling to force dominance, they dance side-to-side, forward and back, collapse in a heap, the player steals an extra metre standing up etc, there is easily a discretionary metre or two in there. And remember, for every extra metre for the "10", it's actually two metres for the defensive line (back & up). Make it 12 metres? It's a huge disadvantage to the defence, it puts them on the immediate back foot as they'll likely still be running back as the ball is played, meaning the runners will be meeting a retreating defensive line. Conversely, set it at 8, and the defence will be ready to sprint off the line before the tackler is even on the ground.
To force the point at how important that 10 metres is, the Storm's wrestling was purely to hold up the ball-player longer so the defence can be set early and be ready to move up off the line fast. Shortening the 10 does the same. And the Roosters are well known for conceding penalties when under pressure defensively (read: with a retreating or staggered defensive line). It shows just how important the mark is for helping & hindering momentum. And like I said, that mark is very, very easy to manipulate.