You are off by a generation. The Greatest Generation was born in the 1920s. This was the generation that produced the Boomers.
I knew my great grandparents. Most were born in the last part of the 1800s and lived through the First World War as young adults. They always seemed significantly less scarred by the Great Depression than their children (the Greatest Generation). There was a communist undercurrent to the Greatest Generation but they didn't get it from their parents.
Lost Generation: adults during WW1
Greatest Generation: adults during WW2
Silent Generation: children during WW2
People born in the 20's would be split between Greatest & Silent.