In the past two years I have inadvertently preformed an experiment on my six fantail goldfish (now seven). I have come to the conclusion that the size of tank they live in for their first few months is directly related to the rate of growth they maintain throughout their life and I can hypothesize that it relates to their maximum size as well. Bear in mind that this is not truly a scientific experiment because their diet has also changed over this time period which may have caused certain fish to grow larger and faster. All measurements are body length only.
Holly, Hazel and Maple were purchased in June 2010. They were “average baby-size” fantails, an inch or less. They were placed in a 30 gallon tank where they lived until December 2011. During that time they grew to about 4”.
Ash and Willow were purchased in August 2010. They were very tiny, 1/2” long. They were placed in a 10 gallon tank because for some reason I thought they were too small for a larger tank. They grew very slowly, 6-8 weeks later they were placed in 29 gallons along with another fish. In December 2011 they were moved to a 125 gallon tank. They were roughly an inch long.
(Here’s the kicker) Zelkova was purchased 1/28/2012 He was ½” long. He was placed alone into a 55 gallon tank. Two weeks later when I added Ash and Willow to the tank he was the same size as them (1 inch). Now today he is much larger than Ash and Willow and grows noticeably daily. Bear in mind that Ash and Willow are at least 1.5 years older than Zel.
The fish who as a baby was given the most room is growing the fastest, the two fish in the smallest accommodations are growing the slowest.
I chose to report my findings only on the fantails because they are all petshop culls and being the same breed have roughly the same potential but my theory holds true with all my other fish as well. Aspen at 11 months is larger than all other, older orandas- she grew up in 55 and was quickly moved to 125 gal. The largest fish of all are my ranchus who until last month lived there entire lives in ponds many hundreds of gallons.

My conclusion is that while 20 gallons for the first fish and 10 for each additional fish is the minimum requirements a 30 gallon tank is less than ideal for three fancy goldfish. Today I am banishing my 10 gallon iso, instead I’ll be using a 30 gallon for isolation so that no baby fish spends any time in a small tank.

Does anyone have any evidence that confirms or refutes my findings?

I am of the opinion that "infancy" in fish is just as crucial as infancy in mammals. It's unfortunate that most people start out with babies and are most inexperienced while the fish are young. Personally I think buying a small tank and waiting for the fish to outgrow it is doing a lot of harm (although of course, sometimes it can't be helped). I will be very interested to hear what the vets have to say.

Yes, this has all been proven true by so many others before any of us, hence, the minimum requirement and the constant advice AGAINST upgrading according to how the fish grow. Because obviously, how would you know when to upgrade if your fish aren't growing as a result of being kept in something too small?