Good thread, Proud Texan, but i'm afraid that what you have heard is 99% wrong.
Have you ever heard of 'Old Tank Syndrome'? Have a read of the link below as it explains how it is entirely possible to have fish living in a tank which receives no water changes at all, but it certainly doesn't mean that they are healthy or happy. I suppose it depends on what you mean by 'need' a water change.
[URL="http
/www.bestfish.com/oldtank.html"]http
/www.bestfish.com/oldtank.html[/URL]
A self-contained eco-system, theoretically should be possible to achieve but in practice it is almost impossible, or certainly at least impractical, as Andywg says. Obviously the filter bacteria which we all know and love take care of the ammonia and nitrite. Plants can take care of nitrate but won't always do so as they prefer to feed on ammonia. Therefore, the tank would definitely need to be lightly stocked to avoid a high nitrate build up.
As previously mentioned there is then the dissolved mineral content ot Total Dissolved Solids (TDS) as it is commonly known. An ever increasing TDS is not good for fish and is difficult to remove without performing water changes.
Assuming you figure out a way to deal with that, then there are, as Tolak mentioned, household air-bourne pollutants which you maybe don't even consider as a threat to your water quality. The most common ones are probably dust, deoderant, air freshener, cigarette smoke etc etc. Given time these will build up in the water and will obviously cause distress to the fish at the very least.
There would also always be a constant battle against kH and pH crashes due to the acids which are the by-product of the nitrogen cycle taking place in the aquarium filter. This would need to be countered by slow release calcium carbonate (or similar) based decor or substrate or by some other means.
As you can see, its not quite as easy as just having 300 gallons +.
As the article i linked to above states, it is possible to keep fish in a tank which receives no water changes, and i hear of it all the time, usually with goldfish which are crammed into a 5 gallon bowl for 10 years (don't get me started), but it is through ignorance that people think this is ok, not education.
The self-contained eco-system you speak of is theoretically possible, but almost impossible to actually achieve. Anyone can keep fish in a tank with no water changes, almost nobody can create the perfect self maintaining tank.
Even if it could be done, it would be due to the filtration devices put in place (including live plants, activated carbon etc etc), very careful stocking ratios, careful regulation of the pH and hardness of the water and measures which would have to be taken to eradicate the possibility of contamination from the world outside the tank, and certainly nothing to do with the fact that the tank is over 300 gallons.
Hope this helps you.
Cheers
BTT