It sounds to me like you are mixing the concepts of
trust,
accountability,
tribalism and
pathological cronyism.
Personal vouching for other people generally is the best guarantee for performance in absence of better criteria.
Trust is not a bad thing.
Trust does not alone degrade accountability. But you need to have a second accountability mechanism in place. Trust, but observe is the classical zen guidance into holding accountability within a group.
Then the group dynamics kick in - tribalism and pathological cronyism.
Exclusive clubs are a typical organization principle in the human species and they increase efficiency within the group by increasing trust and improving the quality of communication through larger shared background. Tribalism alone is not a problem to members within the group.
To agents external to the specific group tribalism may manifest in many negative ways, of course, but it is totally context sensitive if it's a problem or not in the general sense. Many elite organizations, for example, exhibit highly tribal behavior.
Then we get to the black sheep of the lot, pathological cronyism. I think we all can agree without further explanations why it's bad, but, the prerequisites for the pathological cronyism are many of the same kind as needed for the positive patterns exhibited in human socities, including trust and tribalism.
The thing that keeps everything from collapsing into a self-satisfied old boys network is accountability.
But using trust - instead of, say, bureaucracy - as one of the key ingredients of a company culture sounds to me totally great.