As an assistant, you are expected to be diplomatic and discreet in the workplace and when socialising.
You are in a unique position because of all the information that you handle. You need to be careful about what you say, who you say it to, and where you say it. Do not join in employee gossip, and never discuss sensitive information in a public setting. Be diplomatic about refusing to join the gossip. Reject the action but not the people.
As you separate important information from the unimportant, you will stumble across intriguing correspondence that you do not fully understand. You must resist the urge to investigate the information or jump to conclusions. Simply pass along information without asking hypothetical questions. Employers expect this level of discretion from a personal assistant.