Does lifting strength even matter in a fighting context?

Pretty often I've seen such statements as "lifting strength is irrelevant, it's not a weightlifting competition, it's a, fight, where lifting isn't equal to striking".

Question – is that true? Or a common misconception? Because I've also heard a counterpoint for that statement, such as "lifting strength still does matter in a fight when it comes down to wrestling and grappling, as well as to such things as choking someone by grabbing and squeezing his/her throat in a grip, or your typical neck snap cliché".