I'll be blunt.
Dogs barking are extremely annoying to non dog owners. If your dog is barking, it is likely annoying your neighbour. There is no good time for a dog to bark. Not in the morning, not in the evening, not during the working day, at the weekend, at night. There is no socially acceptable time.
You are obviously not bothered by it or you would have a dog, but some people are, and the law is on their side. Everyone has the right to quiet enjoyment of their own home and that means (relative) peace and quiet. Environmental health are there to enforce this. Conversely, there is no legal right to keep a pet.
Your neighbour was probably pushed to her limit to come round and complain. It's good that you've taken her complaint seriously. Out of interest, what do you plan to do to reduce the noise made by your dog?
On the renting / owning thing, you are absolutely correct in your observation. She was threatening you and not very subtly. Sadly the fact is that (assuming you're on a standard AST) your rights as a renter are minimal. I am fortunate to no longer rent but in the many years I did at high city centre prices, I had many a conversation with neighbours who took the same superior view as yours. Nothing you can do about it I'm afraid, unfair as it is.
Focus your energies on some dog training unless you want more little chats along the same lines.