I think what they're trying to get at is that they can't be held liable for damage caused by a pothole that appears within a matter of hours caused by heavy rain etc... Which is probably fair enough - they can't anticipate road damage as it occurs.
That said, it f**ken sucks that they'll deny responsibility for months & then still not fix it up. Take some more photos of the pothole as it is today (or tomorrow) & use that as an argument against their "inspect, notify, repair timeline" policy... If they were serious about fixing road defects within a short timeframe after becoming aware if them, they would have sorted it out by now...