First of all this has nothing to do with any updates to the car. The cars are working fine and this doesn't affect the car's software at all. That would have been clear to anybody with a tech background who would know that the concept of an API being down made no sense, but for the rest of you, NOTHING HAPPENED TO THE CAR OR ITS SOFTWARE.
There was a network issue for the phone app, leaving owners in the unfortunate position of being like 100% (in rounded terms) of other car owners who have to make due without an app to talk to their cars. The issue has been fixed. It didn't keep anybody from using the cars. It didn't affect the car itself at all. It affected the ability to get information about the car from Tesla's servers, but anybody could have used the car as one normally would have. There might have been a tiny portion of the population that couldn't enable keyless driving when they forgot their fob or left it home, in which case they were almost as inconvenienced as any other car owner who left a fob home -- except they could still call Tesla toll free and have Tesla let them in. The car was communicating with Tesla just fine. It was people's phones not talking to Tesla's servers that was the issue.
People may have tried to reboot their cars to get around the problem, but it didn't work because there was no problem with the car's software in the first place. One of the biggest advantages of owning a Tesla is that if there ever is a problem with the software, it can be fixed easily and automatically over the air.