GM is legally correct to an extent, as is John Deere. Look, let's clarify things a bit. A consumer would have a property interest in the physical components of the car (e.g., the bolts, the metal pillars, the glass windshield, etc.).
The GM code that causes the engine to work (I'll be generous here and not make a 'crappy cars' joke), IS absolutely subject to copyright. As such, you have no right to jailbreak or otherwise 'use' it other than for its intended uses GM permits. It sucks, but it's how the law works. Work around it if you want, but suffer the consequences accordingly. Argue it should be against the law to force consumers to pay more for certian GM service, but that's a law that--in the future--would change how things are. As is, GM is right.
It's akin to a novel. The author of The Shining is Stephen King, and assuming he hasn't assigned the CopyRight (I doubt he has), then Mr. King is the "owner." If you go and buy a physical hard cover book of The Shining, then you have a property interest in the physical paper and stitching, and a license to read those words. Those words are "yours" in the sense that you are permitted to read them, but you may NOT reproduce them. You can't take your book, go to a copier, and sell bootleg versions of "The Shining" for 1/3rd the cost at Borders or Barnes and Noble. Despite your payment, you do NOT own his words, he has licensed them to you.
Americans are having a problem with this because we, literally, have a car culture that treats cars like people we love and, yes, own. But we don't. And that hurts us. But copyright law is copyright law.