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Research doesn't show that contract years don't exist, it shows that the best explanation of a spike in the last year of a contract isn't that the person is in the last year of his contract.  This is a claim about what we are warranted in inferring.  Of course, you are right, it's always possible that in Washburn's case the REAL explanation is that he's trying to make a buck.  We might find independent evidence that corroborates this hypothesis, but, on the basis of the evidence we have (you may have more), we aren't entitled to infer it, and hence we shouldn't do so.
Second, as regards projection, you are running together two different things.  1) what a person will do and 2) what I'm entitled to project on the basis of past events.  Nobody is denying outliers, nor are they denying that there is some explanation for why those individuals are outliers.  What people are denying is that we can antecedently predict who will be an outlier (precisely because we don't have adequate evidence about what the explanation is for why the outlier is an outlier). If we only classify players by standardly available statistical pitching categories, then there appears to be no evidence of contract years.  So, for you to form a meaningful projection, you need to first have different categories for typing players so that you at least get statistical reliability linked to those categories that can be predictive of "career years", and then you need to posit a plausble causal explanation for why we get the results we do given those categories.
As regards actual decision in games, I have never heard a SABR person say that you should never bunt/steal/whatever under some very abstractly characterized set of circumstances.  All that I have read are willing to admit that there can be defeaters to these generalizations like when the pitcher has a really slow motion, the third baseman sucks and the runner on first is fast as hell.  What I have seen people criticise is managers who make decisions to bunt in certain circumstances when the obvious potential defeaters to the broad generalization that you should not bunt in those circumstances aren't in play.  I don't think any SABR person would have qualms with a manager who explained that Ichiro is different from the MLB average player and hence the generalization didn't apply.