I agree with Person B in the examples you provided. Person A sounds like an abuse apologist and reading that conversation was a bit upsetting in that regard. I think that "family" are the people that you feel a strong, natural, innate kinship to - regardless of biological relation or lack thereof. I grew up in a toxic family and am no longer in contact with any of my surviving blood relatives. My true family, as I see it, consists of my husband, his (truly awesome) biological family, and my closest friends.

So yes, in answer to your original question, I agree with you and don't think your position is odd in the slightest.