What I have always found interesting is that when you remove talking and social status and the other things that people tend to gauge another's "trustworthiness" and you just have in-the-body to go by, you can develop a deep level of trust and appreciation for a person who you otherwise know virtually nothing about.
Via meeting people on the mat over the years, there are people around the world I count as friends and would literally trust my life with OFF as well as on the mat yet have significant world-view differences with - because we trust each other, we respect each other and can agree to disagree.
The way I often think of this is 'actions speak louder than words'. You can have long conversations with people and still only know who they want you to think they are, or even if they're honest, who they think they are. In the case of trustworthiness, someone may tell you they're trustworthy, but those are the kinds of words that are meaningless. On the mat you can see for yourself who's trustworthy (and who's NOT!). You also get to know people a different way -- again, you see more how they actually act and react to things.