True. The ethics of care is probably best understood as a response to carving ethics up into the (then) mainstream "big three" ethical frameworks.
Deontology is primarily concerned with rules, duties, etc. on the basis of them qualifying as correct moral rules, duties, etc. in principle. For instance, the more rule/duty might be derived analytically (e.g. Kant's categorical imperative). It might also cover an action type that is itself thought to be intrinsically right or wrong by its nature.
Consequentialism is primarily concerned with results of actions or rules, not their intrinsic nature. It is because such and such an action or rule produces the best results (where 'best' is defined differently according to different consequentialists) that it is morally correct. Still, there are typically two central rules at the center of consequentialism: (1) an act is right if and only if it produces the best consequences, and (2) the best consequences are those that [insert value theory].
Virtue theory is more flexible, and probably less of a target for the ethics of care response. It is primarily concerned with the character of the actor--an act is right if and only if it is that which a virtuous person would do in that situation (where the right side gets filled out in different ways).
But the ethics of care is insufficient to be a whole moral framework on its own. I think it is best understood as a supplement to these more traditional ways of thinking about morality and justice. Ethics of care proponents thought the emphasis on principles justice and rigid moral rules was unfounded and missed a lot of the moral fabric of actual situations. Set aside whether that is true. The point is that, yes, an ethics of care proponent is not going to be super excited about a "set of rules" to begin with, let alone a set of rules that undermines the ability to take a sympathetic stance to other moral agents.