I'd push back on the idea that "honestly" implies previous statements to be dishonest. Particularly in corporate contexts it implies that the previous statements were sanitised - either they were moderated in tone to match corporate communication standards, or they were partial redacted due to disclosure concerns.

Once the "honestly" is deployed, you have passed into my circle of trust, and are now privy to the pure, unvarnished version of events, not the glossy version management expects to be projected towards outsiders.

This is expected in any level of people management, you are constantly balancing conflicting desires and priorities.