No it is a common misunderstanding of the phrase similar to duct tape being called duck tape.
The correct phrase is “toe the line,” which means to conform to rules or standards. “Tow the line” is a common misspelling of this idiom.
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Toe the Line vs Tow the Line: Clearing Up the Confusion
Oct 14, 2024 Learn why “toe the line” means to follow rules or expectations, while “tow the line” is a common error with no meaning.
It has a (different) meaning. I used it NOT in the sense of "adhere to gen.-acc. rules or soc. norms." Rather, I used the expr. "TOW the line" - synonymous with "pull one's weight." My expr. comes from "a team of men pulling a barge - and every man pulling his weight."
Sep. idioms with diff. meanings.
To assert that "tow the line" is WITHOUT meaning, as you have done, is invalid.
But thanks for your input; this case does, indeed, resemble an "eggcorn" and I understand your confusion and always welcome an invigorating conversation about word-meanings!
Regards,