Thanks for the warm welcome..
Tadploe, You don't say that little pond has had 3 3-4" koi in it since last spring, 2 Comets 1-2 " long all are doing great WITH NO FILTER I can take a pic if you like.The water is crystal clear with no measurable N P or ammonia... You see mother nature has been ponding far longer than any of us and will strike a balance with fish plants and micro life. Once you try a pond with no filter you will never want one of those oxygen sucking, spewing Nitrate\Nitrogen back into the water column. Not only that they cloud the water!
Now I am not trying to get anyone to get rid of there filter if you want to use one by all means go for it, But please don't try to tell me it will not support any life as I know for a fact that is an erroneous statement.. 
It was never stated that a pond that small would not support life. A thimble full of water will support life. What was stated was PERMANENT ponds of such small capacity do not exist in nature; and it is because, as you stated, mother nature knows what she is doing and has refined the processes involved over millions of years.
Mother nature does provide bioconversion, but only at a level that will support a healthy population of aquatic fauna. Certain parameters are required to support this bioconversion level. First (and most important) is water surface area, for this is where Oxygen is obtained through gaseous transfer. Sufficient Oxygen levels are critical not only for the fish, but primarily for the nitrifying bacteria. Secondly in importance is the surface area of the underwater substrate upon which nitirifying bacteria will colonize. This surface area is much greater in a natural pond with a sand or gravel substrate than in a bare surface fabricated pond. Granted that you may have sufficient bacteria at present colonizing the surfaces of your pond and the rhizospheres of your plants to adequately support a population of 5 baby fish, but these fish will grow and with this growth will be an increased Oxygen demand and a greater nutrient load added to the water column. At some point in the future a tipping point will be reached, as the fish grow larger, where the bacteria level cannot cope with the additional nutrients and you will experience algae blooms, reduced Oxygen levels, fish stress and possible mortality.
This is why biofiltration (more correctly termed bioconversion) units are necessary. These are not unnatural. They are providing the same function for a fabricated system that mother nature would provide for a naturally occurring permanent body of water.
The unnatural list would include: UV clarifiers, chemical treatments, copper ionizers, ultra-sonic algae control devices, ad nauseum.
I sincerely wish you the best of luck.
