Such logic would have precluded folks letting their children take the polio vaccine.Because it uses the same logic that if your Great Grandmother didn't use it, then there's something likely suspect about it's use.
My great grandparents generally died young, as perhaps many of your great grandparents did. The idea that great grandparents should be used as some sort of paragon of healthfulness is ludicrous.
Beyond that, my great grandparents walked everywhere, so such logic would as strongly advise you against ever driving a car, or riding in a bus, to go to work, to school, to shopping, etc. My great grandparents never flew in an airplane; never stayed overnight to visit an amusement park; etc. There are so many things that we do today that our great grandparents never did, yet we still do them, despite the fact that we could fabricate some kind of feigned advice from the past in their name.
This leads to the inescapable conclusion that such baseless folksy advisories are nothing short of a cynical attempt to deceive casual listeners/readers into thinking that there is unfounded credibility in what is being advised. (The deception is not necessarily the intention of the folks who repeat such things, but probably played a part in the crafting of the rejoinder by the folks who came up with them in the first place.) Not only are such things deceptive, but also potentially damaging. It leads people to allow their rational thinking be trumped by sentimental derailments. Emotion is a very strong foundation for making decisions about how to feel, what to value, how to interact and treat others. In a complementary manner, our rational mind is the strong foundation for making decisions about what we do, how we do things, what approaches we take to achieve our goals. Each aspect has its place. Allowing one's emotions to trump their logic on all matters, instead of only matters of the heart, is self-destructive.
If we can establish a rational foundation for things -- great. "This causes X% more damage to this body organ, resulting in Y% more premature death than this other thing." That's a rule-of-thumb I can get behind. But my great grandparents, and I suspect yours as well, would more more likely to advice us to think! To not eschew the advancements of society that make life better, and to only eschew aspects that are actually demonstrably no good!