A lack of trust is usually picked up without any specific reason. It's in the air. One of the most basic of human behaviors is to evade blame and that is why one must avoid if possible by preemption any kind of finger being pointed one's way. Nothing good ever comes of being the one who made the mistake. CYA is the only rational approach. There are very few areas where there is protection when mistakes are made and certainly not in the private sector where politics goes hand in hand with performance.
Gossip - not interested. Rumor - not interested. Show initiative - be very careful. Make sure everybody knows what is what and avoid being the one to decide without substantial evidence and backing in writing.
Any decision must be as obvious to the person questioning the decision as it was to the person making the decision, even if it is a coin toss.
An inspiring story for a change.