It's true there are lots of trails at Nam Cat Tien, most of which hardly anyone uses, and you don't have to have a guide. You can camp near the visitor centre (probably have to pay about $5?) but I'm sure "wild" camping would be frowned upon in any national park.The price of rooms has recently decreased at NCT to about $15.
It's interesting that's there's no mention of birds in this thread, so I'm guessing Jan is more interested in a wilderness experience (camping, purifying water, lighting campfires?, catching own food? not encountering too many locals or "elderly UK" birdwatchers?) and that's hard in a small country with 100 million people.
I mean I am really most interested in being left alone
As a rule, I do not light fires (I would only in a the case such activity would be needed for my or my groups' survival or safety, which has however never happened to me) and I also am not good enough to catch my own food, so I bring it in with me (and pack out the trash so created). I have mentioned camping only because it is usually the way to achieve the abovementioned state of being left alone, as any other form of accommodation usually explicitly requires dealing with someone who provides it - again (and I know it's getting old by now), cudos to Taman Negara and their "Bumbuns", a self-service non-camping wilderness accommodation. I have never met anything like that elsewhere, but I would be more than happy to use such a thing anywhere, it's awesome and it is less intrusive than camping, so the wildlife comes closer to you.
Regarding the motivations - being able to hike into the jungle, set camp and then enjoy the wilderness through the night is one of the greatest experiences you can ever enjoy, regardless of which specific bird or mammal species you actually see. That's why I rank places where this is possible so high. That having said, being able to access wild rainforest freely without a guide even while being confined sleeping-wise to a designated location (as long as it is a nice place) is the next best thing, so the suggestion of such location is still very valuable to me.
In general, I see quite a bit of frown upon camping from several responses in the thread, which I find quite odd. Obviously, wild camping just anywhere has the potential to damage vegetation, cause erosion and stuff, which is undesirable, so the best case situation is when suitable campsites exist. I am almost afraid to say that at this point, but this is, again, what Taman Negara provides, so it is provably possible in rainforest. However even in the absence of those, dispersed camping is a well-proven concept and works even in highly-visited parks in the US: if the number of people wild camping is small, sites are not used over and over and people behave respectfully, is the impact really worse than that of building a lodge and ferrying people to it?