Are allylic three degree alcohols oxidized by the Jones' reagent via a classical carbocation intermediate? I know the mechanism for Jones' oxidation is (picture from Organic Chemistry by Clayden):



and it proceeds through a chromate ester. And in general we understand that the Jones' reagent $\ce{H2CrO4}$ cannot oxidize three degree alcohols. 

However, in my book, a question asked to oxidize the following three degree, allylic alcohol:



The solution proceeded via a carbocation intermediate to eventually form 3-methylcyclohex-2-en-1-one.

I wish to ask if this a correct solution. Does this reaction really occur? That too in the way it is described? If so, why isn't it described in any other book, even as an exceptional case? (Most other books simply accept that three degree alcohols cannot be oxidised) Or is this a by-product or a low-yield reaction?



Source: MS Chouhan; Advanced Problems In Organic Chemistry; 11th ed; Q19; Alcohols, Ethers, Epoxides
It makes sense. Jones's oxidation occurs in presence of a strong acid. Hence, the oxygen can get protonated and leave as a water molecule, giving rise to a tertiary carbocation. The charge can then delocalize, the secondary alcohol get formed, and this alcohol then undergo oxidation. The oxidation will probably drive the equilibrium towards the product.