No it doesn't. DNS breaks as soon as TTLs run out. It's your choice to set them so low that stuff breaks immediately.
I haven't followed this closely, but have there been any... shall we say plain outages longer than six hours? That's not an outrageous TTL. Or a day.
Long version:
If you're so popular all around that you really really want a very very short TTL, people will query all the time from all the places that "count", won't they? So it's gonna be cached.
If you're not so popular or not all around, what does it matter even if you had a very very short TTL? You're not loosing much.