Long Answer:
I've done plenty of tank changes and never experienced an ammonia spike in a tank that was set up correctly in the first place.
My very first tank was (un beknown to me), fish in cycled. I also wasn't as efficient at gravel cleaning and such. I would imagine that at gravel surface level there was a small amount of ammonia being produce from general waste, and that generally the bacteria attached in many places other than just the filter.
When I upgraded from 60l-125l I had no ammonia spike at all and that was with 80%-90% fresh tap water.
When I changed from gravel to sand I did have a spike.
When I changed from 125l back to a 60l I had no spike (80%-90% new water)
When I switched to my most recent 60l I had no spike (again 80=90% new water)
Equally when I cycled the filter for my apistos in 5l of water (the water literally just covered the filter) I set up my new apisto tank with 100% new water and new substrate, I added dechlor and let it get to temp. I then added my cycled filter and fish around 1 hour later, I had no spikes.
When I say 'mature water is a creation of older hobbyists', I'm not just going by the above. But also other peoples experiences and scientific fact.
To the person who said...
but then again how many times have scientists revealed to us new discoveries completely contrary to what long held beliefs use to be?
That as a comment is a fair point, but in this context it isn't applicable. We know exactly what type of bacteria carrying out the nitrogen cycle, and we know they're not freeliving. They colonise on surfaces that have high O2 and water flow (as Oldman said). This is fact, it has been proven beyond doubt... it is no longer just 'a theory'.
There will at any one time be a few bacteria floating around in the water that are either dying and have come loose from their colony, or have just come loose generally. But they are not free living normally, and the number floating around are negligible.
The only 'mature water' I could say exists is in relation to how long fish have gone without a water change. If the fish have been in the same water for a long period of time then it starts to differ greatly from the tap water conditions. Therefore any big water changes and such can cause problems etc.
THIS is where the theory of 'mature water' came from with old hobbyists. Because regular water changes weren't the done thing. And when you eventually did do one it often resulted in fish deaths because of (presumably) things such as pH shock down to the extremely differing values of TDS between tap and tank.
Oh and just one more thing to add, although mature water doesn't exist, mature tanks do. There is more to a balanced aquarium than just a biofilter (Which does become more stable over the first 6 months), lots of other factors keep a tank balanced. These are the 'unknowns' but the theory is that there are probably other colonies of bacteria and micro organisms that coat surfaces such as gravel and tank walls and affect things that we don't measure.
Imparticular in a new tank you tend to get them growing on the tank sealant, presumably as they 'eat' up anything leeching from it.
But as these things don't noticably effect the fish, and the link is clearly showing there is nothing beneficial in the water, it's very easy to explain and understand why mature water doesn't exist.
Short Answer:
No mature water doesn't exist, particularly with respect to the nitrogen cycle and avoiding tank spikes.
Edit: Just to add, sorry if I've repeated anything anyone else has said. But I figured it wouldn't do any harm
