Is it true that Milwaukee tools bought through Amazon are not covered by Milwaukee's warranty?

A number of people say they have contacted Milwaukee and been told that Amazon is not an authorized retailer and tools bought through them will not be covered by warranty. A Google search showed that they were even the subject of a lawsuit a few years ago, but I couldn't find details on the outcome.

Home Depot always has better prices anyway, but it's certainly worth noting if true.

Edit: Actually, Amazon currently lists the M12 3/8" cordless drill for $45, Home Depot wants $89. That's a big difference.