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They don't release their exact statistics, but Conversion Rate Experts are pretty authoritative on the subject of scrolling vs. fold.

http://www.conversion-rate-experts.com/scrolling-tips/

  In split tests, long pages often beat shorter pages.

  As a rule of thumb, your page should contain at least as 
  many words as you’d use when selling your product or
  service face to face.  

  The winning page we designed for SEOmoz was six times 
  longer than the control, which it outperformed by 52%.

  Whenever someone tells you that they’d never buy from a 
  long page, remind them how long Amazon’s pages are.

  Long pages are effective, but only if your users know that
  they can scroll and are given compelling reasons to do so.

http://www.conversion-rate-experts.com/crazy-egg-case-study/

  The redesigned page is about 20 times as long as the
  control... new page outperformed the control by 30%.

http://www.marketingexperiments.com/improving-website-conver...

  In our initial micro-test, long copy outperformed short 
  copy by 40.54%. Click-through traffic sent to the short
  copy page was unprofitable (-14% ROI), while traffic sent
  to the long copy page produced an ROI of 21%.

http://conversionxl.com/4-cases-where-short-home-pages-outpe...

  Short copy performs better when there is low perceived
  risk, low cost, and low commitment... when the customer 
  has an emotional, impulsive, and “want-oriented” 
  motivation. When you want people to take action that 
  doesn’t cost them dollars (email signups, free trial,
  clickthrough)

http://blog.clicktale.com/2007/10/05/clicktale-scrolling-res...

  Visitors are equally likely to scan the entire page no
  matter the page size.

  Below 540 pixels, both visitor attention and page exposure
  decline exponentially.

On the other side, are lots of Web 2.0 A/B testing results that basically say, shorter is better.

I might have missed that one. Could you provide a representative link or three?

I'd speculate that it's generally easier for people to not decide and conserve their willpower, but we still gravitate towards ‘decision mode’ when about to do something that looks irreversible. Two common cases:

a) Easily reversible or just insignificant action, no commitment—you offer a free product or trial, or a paid service that could be easily cancelled. Long copy would turn on ‘decision mode’, but we may want to avoid that, so less info is probably better.

Example: Lots of ‘Web 2.0’ services.

b) Not easily reversible action—money are required up front, or you're upselling something to free users. Regular people (not yet fans of your product) are likely to consider different options in this case. Long and good copy, therefore, would present more and more reasons to pay.

Example: Apple website.

That said, I'd like to see a study too.

I am positively desperate for some kind of researched and statistically backed-up explanation that figures out the factors on both sides!

Why don't you learn to write copy and test it yourself? You will arrive to the same conclusion that every industry veteran arrives to: long copy out sells short copy. Why? Everyone has different hypothesis. Mine is that long copy allows for the writer to disqualify prospects and attack all buying objections right from the start. When you have those two things working for you, the decision to buy mostly boils down to how attractive the product is to the prospect. Try it out. Learn it. I'll even teach you the basic if you want. If you can program, this stuff is cake. email in profile.