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1. Air intake has engine breather tube. 2. Gases from engine contain vapours from combustion. 3. This condenses inside the inlet manifold creating an oily liquid, over time it accumulates enough to pass the gasket. Place your hand underneath the back of the inlet manifold, if it's wet with 'oil' there's the problem. Ideally set up a catch tank to contain this before it enters the inlet manifold, they are cheap enough. This is mine on the 2.5v6 (which is easier to do).

Ok, just to be sure, we are talking about the intake manifold tuning valves. They don't look too hard to get to once the windshield wipers, plastic cover, and brace are removed.

After searching in the car and online it appears that a NAS 2004 3.0 v6 does not have flapper valves anywhere near engine oil. They are on the back of the intake manifold. Unless there is something else I am unaware of it is looking like the back of the valve cover is leaking, but only when it is cold.