Plot hole: Despite the plot, Lucy couldn't be fooled by Jimmy and Timmy Hudson. True, they could be fraternal twins but not even Lucy could mistake them for being identical as one's got a higher voice and the other's shorter.

I Love Lucy (1951)
1 plot hole in The Amatuer Hour - chronological order
Starring: Lucille Ball, Desi Arnaz, Vivian Vance, William Frawley

The Séance - S1-E7
Continuity mistake: After Lucy tells Mr. Merriweather that he's invited to the seance, when it cuts to Lucy unfolding the card table legs, note the couch behind her with one normal seat cushion on the left, but in the next wideshot there's an additional shorter cushion under the normal cushion. The small towel also repositions itself neatly on the couch. (00:11:55)
Ethel Mertz: Rome wasn't built in a day.
Fred Mertz: Well, Rome wasn't built like you either.
Trivia: Lucy, Ricky, Ethel, and Fred all do the impressions of Maurice Chevalier. Thirty-six years later, the same impression is done in the 11th episode of The Simpsons.
More questions & answers from I Love Lucy





Answer: There is no reason. It's a just a silly plot device, typical of the era. Women characters were often portrayed as making uninformed assumptions or decisions.
raywest ★