That was my interpretation when I first read the detailed process about the BLS survey.
It will still measure inflation, but if the median American's spending preferences changes when prices change (which is true until the median American can never afford anything except the bare necessities to begin with), then those changing preferences will result in falsely lower inflation numbers. Combined with Hedonic adjustments, true inflation has probably been about 50% higher than reported for the last two decades (and more in line with the Big Mac index) [0].
It will still measure inflation, but if the median American's spending preferences changes when prices change (which is true until the median American can never afford anything except the bare necessities to begin with), then those changing preferences will result in falsely lower inflation numbers. Combined with Hedonic adjustments, true inflation has probably been about 50% higher than reported for the last two decades (and more in line with the Big Mac index) [0].
[0] https://medium.datadriveninvestor.com/what-do-big-mac-prices...