If I am following you correctly then I definitely agree that "necessary" and "sufficient" are very relevant terms. However I think where this goes is that simply using those terms does not really advance the ball to the ultimate conclusion, which is understanding when we can confidently apply those terms, and why we are confident in applying them in a particular situation. Ultimately in every case we have a conceptual issue of what happens at the limit of our ability to observe directly. Is it proper to conclude that 'seeing is believing' is the appropriate standard of considering something to be true? At what point are we confident in going further to make a confident statement about something that we can and probably never will observe directly.
Here's something else that is relevant, a jibe from Cicero, in his "On the Nature of the Gods." This is a jibe, but it is easy to see how an Epicurean might appear to be overly confident to a skeptic. I think what we're looking for here is first an understanding of the ancient Epicurean position on when to be confident and when not to be, and then we have to decide for ourselves which we are "confident" to adopt:
QuoteHereupon Velleius began, in the confident manner (I need not say) that is customary with Epicureans, afraid of nothing so much as lest he should appear to have doubts about anything. One would have supposed he had just come down from the assembly of the gods in the intermundane spaces of Epicurus! “I am not going to expound to you doctrines that are mere baseless figments of the imagination, such as the artisan deity and world-builder of Plato's Timaeus, or that old hag of a fortuneteller the Pronoia (which, we may render ‘Providence’) of the Stoics; nor yet a world endowed with a mind and senses of its own, a spherical, rotatory god of burning fire; these are the marvels and monstrosities of philosophers who do not reason but dream.