I believe that trust can't be taught, it has to be earned. Your behavioral style can create a default for who you trust or don't. Using DISC styles, there are differences in the way certain styles approach trust. Influence and Steadiness trust first until trust is broken, Compliance requires trust to be earned. Dominance doesn't care about trust as long as what's happening now drives their agenda.
Accountability is doing what you said you would and apologizing if you screw up. Imagine a team where there is one person who doesn't work as hard as everyone else and gets away with it. What is the impact on that team? Eventually, the hard working members will see that hard work is not valued. This destroys trust, alignment and performance: team over. The pyramid is like a Jenga game- if blocks get knocked out of the bottom, the top is compromised. Think of a time you worked with people who were all in- accountability was shared by all. It's an amazing and rare experience.
An aligned team is one that has clear roles, shared purpose, and values the ability to work well together. Notice that the base of this pyramid is composed of these components for self (left side) and for team (right side). This is the foundation of a High Performing Team, just like family and community are the foundation of the Irish that I know.