Tesla owner here. Sorry, I'm waaay behind here in the thread. Yes, video can be provided instantly as it's simply recorded on a USB drive. The problem is most Teslas come with a standard 128GB drive which is only 3 hours total and then continuously overwrites the oldest files. Some Tesla owners do add larger storage but most don't. Tesla's security recording consists of two main functions: Dashcam, which records while you are driving, and Sentry Mode, which monitors the vehicle while it is parked.
The issue is it's now been around 150 hours since Nancy went missing. The biggest break in the case would be if the vehicle they were looking for happened to park at the Circle K location next to a Tesla with Sentry mode enabled. That would give a very clear, close up footage of a person getting out and back into their car. Anytime someone parks next to me or in front of me, or even walks next to my Tesla, it records video of them and saves it. Tesla does give you the option to disable or enable the Sentry Mode as it typically consumes 1% to 2% of battery per hour so some owners do turn it off.