This really depends on your area, my wife got rear-ended by an uninsured motorist at the beginning of Feb (see more details below) and since there is only one Tesla certified structural body shop (with a single specialist), there was 5 Tesla's in front of us in the queue and it took over 2 weeks to get an estimate. I read a post this week that the same body shop now has 30 Teslas in the queue and the estimated time is 3 months to get an estimate. As for parts and fix times, that also varies wildly, I've heard of people getting their bumper replaced in a week, and some waiting for parts for months.
It sounds like an urban legend, no sane insurance company would total a Tesla if they could pay $5K to just repair it. Even with diminished value claim their cost would be so much less than totaling even the oldest Tesla made (first Roadsters). It is more likely that something got lost or distorted (as it usually happens with rumors) and someone lost a 0 ($50K, not $5K) or maybe even the initial "visual" body shop estimate was $5K but later turned out to be $50K. As a point of reference, our car's damage visual estimate was $16.5K and of course the insurance company would not even consider totaling the car. Once the repair shop opened the car up and started adding up internal damage, they stopped estimating at $65K and only at that point the insurance declared it a total loss.
Consider yourself lucky that the uninsured motorist living at the motel stopped long enough for the police to interview him. In our case the driver of the car stopped, stumbled out of the car, heard the word "police", said "I ain't going to jail for this", got in the car and drove away. The police went to the address where the car was registered, she no longer lives there, so the investigation is closed. But here is the important part - if it wasn't for dashcam video (and a kind couple who witnessed the accident and stopped to help, but video always beats witness testimony), we couldn't have proved it was the other person fault. If you look at the video of the accident, you can imagine the exact same outcome if it was my wife who drifted into the other person's lane rather than vice versa. If it wasn't for the video, this would be a collision claim, rather than an uninsured motorist claim. The deductible reduction itself on this accident paid for the dashcams in both of our Teslas, not to mention the rate increase we would have been paying for years.
PS> As a point of reference, our damage was significantly more extensive than yours from your pictures. We had front damage (hit a concrete barrier at 60mph - see top left corner of the video which shows front view of the accident), rear damage, airbags popped, the car was not driveable after the collision (HV battery disconnected, all electronics shut off within few hours).
