I actually agree with the notion I think MMF is hinting at here - automatic respect should not be assigned just because of someone's age. Respect is earned. I respect elders just as much as anyone else inasmuch that they are human beings and deserve a modicum of privacy, space, at-worst-neutral treatment, and dignity.
If a person, regardless of age, gender, or race, came up to me and starting harassing at length me about something innocuous, I would reserve the right to mock the person to their face as they have violated my privacy, personal space, and have begun to treat me negatively without me having done anything to them or anyone else to deserve the treatment.
I have met some real idiots who were two to three times my age. Just because someone has managed the rather meager feat of not dying does not mean they are necessarily wiser or worthy of elevated levels of respect. They are just older. Conversation with them may prove otherwise, but, clearly the woman the OP encountered immediately dismissed all pretenses of being wise; she approached someone who was not being threatening, accused the person of being threatening, felt that she had the right/privilege to admonish the person, and continued at some length. Those are the actions of a relatively unpleasant person, and one would be quite wrong to reward her behavior with polite or shamed acceptance.
Anyone who asserts their superiority over you without just cause or qualification can, in the words of Abraham Lincoln, "fuck right off and die."