Presas are confident in their size too. They understand that they are powerful, and don't feel the need to prove it. (from what I hear, I don't own one yet...). So, they don't typically lash out, unless they or the family is attacked.
You can find some training videos online for them that are pretty crazy.
One particular one that I like is where an "intruder" is waving his arms, and yelling at a presa through an open car window. The dog barks, but doesn't move no matter how much the guy yells and waives. But, the moment the guy touches the car, the dog attacks.
You can see how powerful they are in some of the attack scenes too.
Here's a pic of the "Red Star Girls"