Very valid point - and one of the quickest ways to erode team trust. Rather than operating in a safe and secure environment employees engage their "on alert" button, which manifests in the following behaviours:
Unease when colleagues visit the boss's office and shut the door. (What are they talking about - Is it me? What have I done wrong?)
- Guardedness around colleagues who were previously "safe"
- Defensive and accusatory behaviour
- "buttering up" behaviour towards boss
- Lack of enthusiasm for work
- Joining the "gossip" group, or, conversely isolating oneself
As a Manager, demonstrate neutrality, fairness and discretion when dealing with inter-team issues. Taking this approach every single time sends a strong message to the team that you won't be "caught in" and, that they can all expect a fair and impartial relationship.