After 35 years in the industry in various capacities (from architect, engineer, VP, and different products, small and large companies, ...) I can heartily confirm this.

A company with a good culture is like a good football or soccer team. They work with each other to win, they know each other (enough for the job at least).

I am working at a bigger place now and the AI mandates handed down have been quite unproductive... As if we wouldn't have been able ourselves to figure out how to use the new tools - like we have since the beginning of software.

If management trusts you do to your job and has your back, then you trust the management and will naturally do a better job. Now there are always a few people who are exceptions to this, and part of good culture to identify those and remove them.