If it's a warranty repair, I don't see how they would replace the motherboard with anything other than the same model. Besides, I've had cases where Windows manages to boot after replacing the motherboard with a different model.

As said before, they're lying if they say there's no way to get your data before they reinstall. As long as the hard drive isn't broken, it is always possible.

If they claim not to be lying, the only other option is that they're very incompetent.