I understand where you are coming from - but there seems to be genuine disagreement among experts as to which expression is correct. I'd say it's the rare case of BOTH expressions being correct - with somewhat different meanings.
Regards,
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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Vocabulary.com
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grammarmax.com
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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.