The new intro is a nice improvement. I agree with Melcombe about scope (and much else). Some issues I think could be cleared up 
 * Saying non-parametric means "very few" assumptions seems to vague; one could say that assuming a classical linear model is just one assumption. I appreciate that it looks very abstract, but the finite-dimensional restriction is in van der Vaart and Cox [Prinicples book] - and probably lots of other places too. Perhaps a little more in the way of examples would help? 
 * Simple random sampling is an assumption that can be made in fully- semi- and non-parametric models. So it's perhaps not best to state it as the sole example in the non-parametric bullet. 
 * The randomization-based models section should start with something to orient the reader. For example, "An important experimental situation where strong assumptions are well-motivated is the randomized study". Then say how inference proceeds. Then compare randomization-based inference to other approaches. 
 * "warrants" is nowhere near the right word. 
 * False models and pi=22/7 is a bizarre comparison. Anyone can see 22/7 is not Pi. It would be an overstatement to ridicule assuming classical linear models because they're not true. (n.b. I would rather not include the Box mantra on models and usefulness, it's hackneyed and quoted as support by people with very different stances) 
 * Information and computational complexity - doesn't mention inference anywhere, so not obviously relevant 
 * Fiducial/Lindley - Lindley (1958) didn't show fiducial inference "fails", he showed that it didn't correspond to a Bayesian procedure - this isn't quite the same. Don Fraser has written about this (well).