I tagged it as access:delivery=no and as a path instead of a road. The access for emergency staff is also just one of many reasons not to delete private paths, an other one is that other people might see them and not knowing that it's private, so they will just (falsely) map it as public, leading to the issues you described before. I hope the new tagging will help solve the issues. 

I will close this note once again since I don't think there is any reason to change these paths anymore at this point. 