A good trigger is definitely a big piece in the puzzle. It is the part you interact with the most on a firearm. If it's too heavy or sloppy, then you will have to compensate for this, taking focus away from the objective of making a well placed shot.
Focusing on the trigger is fundamental to making a good shot - anything that makes you concentrate on the trigger WILL make you a better shooter. Squeeze of the trigger is not a natural motion - it has to be learned and practiced and practiced, and practiced again. With longer/heavier tirgger you'll be able to see the sight picture drift and correct the mistakes, with light trigger you'll just get "unexplained" flyers.
Don't get me wrong, it's nice to have a "good" trigger and it will make good shooter's job easier - but claiming that trigger universally affects accuracy IMHO is misleading.
P.S. I have to admit, that over the years I had to say it a few times - "you got to do something about this trigger" - but we are talking about over 10lb pull.