We have a much-beloved piece of legislation here in NZ called the Consumer Guarantees Act By law, a seller can't require you to produce a receipt (although evidence that you are the purchaser through other means - i.e. bank or credit card statement, can help your case if there is a dispute). They cannot refuse to remedy ANY problem with almost anything sold. It's got to do what it's meant to do ("be fit for purpose", for a reasonable time - often longer than offered warranties), or else the person who sold it has to put it right. It's wonderful. Just mentioning the CGA is often enough to get a retailer to sort it out, because if it goes to court, retailers almost always lose.
Love it. Here, of course, once there's been a recall the manufacturer can't request a receipt at all because date of purchase doesn't matter. If they don't have conclusive proof that they've fixed it already, they're required by law to fix it. Which didn't stop Bosch from being extra-douchey about it but once the magnitude of the issue was rubbed in their face, they got civil.