I wouldn't exactly jump ship just yet. While that is a fine mechanism suggested by Stewie (though a little sloppy), the alternate carbocation mechanism has not been disproven. If you were to do a Jones oxidation of but-3-en-2-ol, I think the major product is methyl vinyl ketone (this is not the preferred MVK prep). I don't know that crotonic acid does not form, but I don't think it is a significant product. I think the equilibrium of the chromate ester should still favor the more substituted alkene if a facile electrocyclic equilibrium were present. I am not ruling out the electrocyclic reaction per se, but I'd like to see stronger proof for it. I don't think of pyridinium chlorochromate as acidic. Does it give the same product? We could also dispute the leaving group, whether it is water or chromic acid, or chromate.
I am also not so troubled by the Curtin-Hammett thinking either. Obviously, if there was an oxidation path from the tertiary alcohol, then it could be invoked more rationally, but if one were considering the energy levels of the intermediate alcohols in relation to their predicting (or not) the product, then I am not too troubled by it. I would consider understanding the implications of the Curtin-Hammett principle of greater value than a perfect application of it.