Some weird comments on here.
If my car could be opened with a key that wasn’t mine, I’d be getting the system checked and re-coded so that it couldn’t, rather than pouting at the owner of said key. Even if, for the sake of argument, the key had an inherent fault that was sending the wrong codes (or even if the neighbour had some sort of magic door-opening universal remote) ultimately there’s still something inherently insecure about my car’s system that I’d want it sorting. What if the OP gets his key ‘fixed’, what then, how many other keys are there out there that also need fixing?
Those who are saying it’s the neighbour’s problem aren’t being un-neighbourly, they’re correct (if a little blunt perhaps).