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 tertiary alcohols.
However, in my book, a question asked to oxidize the following tertiary 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 tertiary 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