One critic has said that the loosening of the rules that occurred to Offred (cribbage, daughter’s photo, Nick) in reality bonded her tighter to the society. Why?

Offred's "freedoms" are always at the will of the state. The Commander gives her these freedoms but they only tie her further to the system which exploits her. In this sense Offred isn't a heroic character. She understandably takes these gifts which, in the end, validate the role she is given. One can say that by accepting these freedoms, Offred tacitly accepts her enslavement. Taking these favours means she owes something in return. The subtext of her "perks" is that she has bought into the system.