I think she meant that she could trust Chakotay to come up with some lame
bit of folklore that he would falsely claim as a story "told by my people",
no matter what the situation.
Or maybe she meant that she could trust Chakotay to make her look like she
wasn't the very worst actor to ever appear in Trek, after all.
No, wait, she trusted Chakotay to have romantic liasons with even less
chemistry than she had with a holodeck character.
I've got it: she trusted Chakotay to save her from being the least
believable character as commander of a ship. Yeah, that's it.