In general, it implies sincerity, but when suspicious about ones intentions, believing the opposite seems to hold more truth than the alleged truth other individual proposes. It's like their intention does not match substance, but they use the word to try to cover the lie. Could this be an insecurity or co-dependence issue?
The situation is very long to describe, but to make a long story short, I heard the sides of two friends. Many things Friend A has been saying about Friend B have turned out to be complete fabrications and lies, but Friend A continues to use words like "honestly" and other descriptors associated with it in sentence to make it sound more "true." Friend A keeps calling, texting, and emailing Friend B and even parked out in front of gym texting friend B. Friend B wants nothing to do with Friend A, it's looking like a harrassing and stalking situation, yet Friend A denies that situation and the things he said even though I've seen the texts, emails, and voicemessages to prove otherwise. It appears that Friend A is having problems accepting that Friend B will not subject himself to his manipulation. Friend A has a history of being very clingy and needy.