The threshold of tawātur concerns so many narrators in every generation that all agreeing on a lie, or all coincidentally reporting the same falsehood, is ordinarily impossible. The report must also originate in sensory knowledge, such as hearing or seeing.
Mashhūr Hadith has three or more narrators in each generation, but their abundance does not reach tawātur.
A Hadith being widely known today is a different matter: popularity alone does not establish its narrator numbers in each generation.