No, they had it correct; it is "toe the line". It has never been "tow", ever.
This variation of the idiom comes primarily from runners in a race conforming to the rule/standard/practice/doing as expected with putting their toes up to the starting line prior to the race starting. The precursor phrases that are similar and far older were also "toe", but all meant the same thing of conforming to the standard/doing as is expected; e.g. "toe the plank" or "toe the mark".
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