It's obviously true, because Elon would be contradicting it if it weren't. Which he isn't.

Instead he's muddying the issue like so:

"As the State of Charge log shows, the Model S battery never ran out of energy at any time, including when Broder called the flatbed truck." (Technically true and useless)

Broder's towing company further backs him up:

http://jalopnik.com/towing-company-the-nyt-tesla-model-s-was...

They think it was easily avoidable.