The Fed doesn’t calculate CPI, but CPI ‘adjustments’ are indeed fundamentally cherry picked to lower the rate. There are a bunch of crazy mechanics like “hedonistic substitution”, min() functions, and adjustments that by definition can only adjust the rate down and not up (eg ‘quality increase’ in basket of goods = adjust CPI down by the ‘quality increase factor’, but quality decrease does not adjust CPI upwards).

People use the million prices project to argue CPI is correct, but misses the point that the project uses a regresssion model to automatically multiply their index by an adjustment factor to match CPI - and that adjustment factor has only gotten smaller and smaller (ie their index reports higher inflation growth than CPI) as time went on.