i think you're getting the trust causality somewhat backwards. people don't simply fall into trustworthy or untrustworthy buckets, but rather it's mostly context dependent (with rare exception; e.g. sociopaths). a trusting environment can reveal the latent trust inherent in the team members.

and trust takes time to build, so it's often not something you can just hire for (unless maybe you hire a whole team at once).

teams also require a blend of skills blanketing the problem domain, diversity of thought and background, necessary resources, clear goals, and the autonomy to make decisions toward those goals.