I think you are more or less correct in your assessment of the meaning of the entire paragraph when you say "advanced technology made Americans helpless in fixing gadgets or technical things."
But, the part you have underlined speaks about an earlier time when Americans were used to looking after their own needs as evidenced by the portrayal of the American family in early American literature. Readers were familiar with reading about families that were self-reliant and almost "MacGyveresque" (my word, don't bother looking it up, but you can Google MacGyver TV Series) in their ability to fix all things human and spiritual.
I take issue with one thing the author of your text writes: He says "It takes an expert to fix the former (an air conditioner), but not the latter (an over-heated train)". The writer has obviously never ridden on a bullet train (TGV in Europe) in summer.