Sure they can. Just like you don't OWN your copy of Windows (you just have a license to use it),
For reference, you own your copy of Windows. What you don't own is the right to make & distribute copies, which leads to all kinds of weird messes in software law because the courts have misinterpreted the phrase "fixed in a medium of expression" and have interpreted copies in RAM to be "copies". The law in this area is pretty convoluted and poorly understood by a lot of people, including judges, and companies like Microsoft make a point of attempting to mislead people even more about the state of the law. But the key point, if you want to look it up, is First Sale Doctrine.
I'm pretty sure that if push comes to shove, Tesla could say that they are denying you the license to use their software, meaning the car is disabled. Since everything is driven by software, and not enough people (besides us techies) care to fight this, we are going to be at the manufacturer's mercy (for the time being).
I'm quite sure they can't. If we fought that sort of ******** in the court of public opinion, we'd win. If we fought it in court, we'd *also* win...
Tesla sells its cars. (I carefully read the purchase agreement.) A bunch of stuff is implied by 'sale'. (And if you leased your car, you have much less.) As green1 says, they can deny warranty coverage (and they should deny it), they can stop providing software updates (and they shouldn't stop), they can refuse to provide documentation (they should provide documentation) but they can't legally disable a car which you own in fee simple; you'd have grounds to sue for damages if they did.
Check out this
Wired.com article about software licenses, and
this article about John Deere trying to pull a fast one on its customers. I'm only mentioning this so people are aware of this risk before considering buying a salvage vehicle.
The problem is precisely one of "pulling a fast one". I hope Tesla acts reasonable.
Meanwhile, congrats to Yauheni. And thanks to Tesla for being reasonable and helpful to him!
I would warn Yauheni: until you get clear cooperation from Tesla, don't put the 3G card back in, just in case of the remote (ha ha) possibility Tesla tries to disable your car remotely. Without the 3g connection, they can't.
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Is there a report of this actually happening against the owners wishes? I don't think they could legally disable a car without the owners permission. Refusing to service it is one thing, but Tesla doesn't own the car.
I don't think they can legally disable it, but they totally could illegally disable it. Even if that's unlikely, I doubt you want to risk it. So don't take it in until you get their promise in writing that they won't disable it.