with a belief in an elusive incorporeal power pervades the body in order to emphasize asceticism, honesty, and moral training
In Catholic/Christian thinking, "honesty" is something that a person should extend to everyone else. It seems this idea (that an "honest" person is honest to everyone), mostly survives as an expectation for the general modern individual.
Of course, other groups (with a social strategy) see honesty as something that should be extended only within their group -- and they see extending honesty beyond their group as foolish and harmful.
As Epicureans, we each organize our life to spend most of our time among our in-group -- and an Epicurean has very high incentives to be honest with a friend in all cases. Still, I cannot see why an Epicurean would be honest in all cases with someone who is not a friend (particularly if being honest may cause consequence, or if being dishonest may cause benefit).