Replicators were said to convert energy into matter.
No, they're said to convert stores of matter into other forms based on stored molecular patterns. Like the transporter, only instead of sending something from one end to another, you put in enough matter of the various necessary elements and in the proper quantities as input and get whatever it is you want back as output.
Not on-screen.
On-screen dialogue repeatedly states that 'replicators turn energy into matter' (it doesn't get simpler than that).
Okay, I checked into it, and you're right that no episode references what I said about the functioning of replicators. Still though, I can't find that quote anywhere either; I can't actually find any reference in-episode to how precisely a replicator works, let alone repeatedly saying that statement.
However, the closest I could find to explaining how a replicator works, in "Year of Hell", had Janeway say the watch Chakotay replicated represented a meal, a pair of boots, etc., which does seem to support your interpretation more than what I thought. That alongside Timo's point suggests that canonically you're right.
I still would rather it worked like I said, since that seems more logical and efficient to me, but I can't argue with in-show evidence.
