edit - you can also even apply the same technique to try and warn people of bad things. Go wild with it.
I've heard of Florence Nightengale. But I've also heard of Mother Teresa. My knowing even good things about a person doesn't necessarily impact how good of a person they actually were. I remember reading books as a kid with Mother Teresa in them as a totally sanctified figure, but what Christopher Hitchens says about her is probably true, and so she's not worth the respect that I gained for her and carried with me for so long.
I think it is an astute observation. For all I really know, Florence Nightengale was just an unskilled doctor-wannabe who ran around Crimea amputating people without cause. People that I think of as good aren't necessarily so. We have to remain skeptical.
In the long run, by her use of statistics, she invented modern nursing and much of the practice of evidence based medicine, but she got started by establishing a name for herself.
(argument provided for illustrative purposes)
Random people idolised does not equal anything.
As per the best reply to what about..... squirrel.