Remember is a bit of a tricky verb. It can be a reporting verb, in which case the when is a part of the reported speech structure - I remember when he left the room is akin to sentences like I said that he was sleeping or I know when he left.
But most reporting verbs either only link with that and not wh- clauses, do not have usages which take a direct object, or have effectively the same meaning in both cases. Remember does take a direct object, and as you've noted the meaning differs slightly - which causes problems when the entire wh- clause can be interpreted as a noun phrase.
So if you say I remember when he left the room, it's ambiguous whether you're using remember in the direct-object meaning ("to have a memory of"), or as a reporting verb ("to know based on memory"). If you interpret when he left the room as a noun phrase, it's the former - if you link when to remember and treat the sentence as reported speech, it's the latter.