The stock needs proper fit and torque, if the barrel is touching any part of the barrel channel then it isn't free, and wont group tightly.
I would add the old dollar bill test is really not enough room . Meaning if a dollar bill slides freely between the barrel and the stock but just barely thats not enough room . If you can force the barrel and stock to touch by pinching them together with your thumb and fore finger . IMO there is not enough room between the barrel and stock or the stock has to much movement . This could mean the stock is not ridgid enough or is not torqued down properly .
Just my .02