"Hedonic adjustment" is meant to control for the 'quality' of some (limited) products sampled in the CPI such as rent, computers and automobiles. 'quality-adjusted' means that they run a standard linear regression across the features of sampled items to normalize the variation in the sample. For example, the sampled rent of apartments would be modeled as (in the simplest example I can think of) :
y = rent, b = slope, x = sqft
y ~ b + x is the extent of the 'hedonic adjustment'
There don't really exist any control variables for 'better'. Nobody at CPI is subjectively saying toiler paper is better. What they will stochastically estimate is the per-unit price. So if for $10 you get 9 double roles, and last year you got 9 single roles for $10, then the price went down. But I assure you as someone who has looked at row-level data of what the CPI samples and does, there are no cases that are this extreme in the aggregate. They could drop the hedonic adjustments and it would make no practical difference. Private companies use similar sampling methods with better data and don't show wildly different headline inflation (see: Billion Prices Project http://www.thebillionpricesproject.com/)
There is no doubt however that the CPI data is inadequate, has a non-trivial lag, and does not capture true regional differences in prices. Just try using it to adjust your salary if you move from Birmingham to New York City and see how comfortable you'd be. But there is no conspiracy; that would presume far more competency than they have hired for.