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 mistake in The Amatuer Hour - chronological order
Starring: Lucille Ball, Desi Arnaz, Vivian Vance, William Frawley
Ricky Ricardo: What's the matter with you? Are you crazy or something?
Trivia: Fred and Ethel's bickering relationship didn't require much acting; in real life Vivian Vance and William Frawley didn't care for each other at all.
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 ★