Fitz gave their own answer, but I had a thought as well.
One of the rules that gets brought up that rarely makes it into these particular discussions is that you only roll the dice when the outcome is in question. You don't need to roll dexterity to walk down the stairs. It just happens. So... do you need to roll dexterity to walk down the stairs gracefully? If you are playing a 7 ft tall, 800 lbs hippo man do you need to roll constitution to quaff a small barrel of alcohol with limited ill effects?
There is this push to sort of have the tail wag the dog in these conversations sometimes. Your constitution score is only rolled when the outcome is uncertain, yet we also get told that your default state of existence is determined by your score. No matter how big and thick and bad-ass you are, you can't just ignore a teenager punching you unless your con score is "higher". And I put that in quotes because the baseline average is 10... and nearly every adventurer is above a 10.
It just strikes me that you asked a rather odd question. Sort of like someone saying they run down the stairs and then you asking if they have a high enough dexterity score to be allowed to do that. Why wouldn't they? Why can't a hippo man with a 13 or 14 Con, significantly higher than the average, be tough?