All the publisher has to do is arrange for the Kindle edition license to show up automatically in your account. They already do this at Amazon for special Buy One Book, Get a Second Book Free special offers that they have done. I have several books in my account that were obtained as the "free" book (including one where the "buy" book was free by mistake, giving me two free books at once). The only issue is that on the Kindle edition page, it doesn't show that you own it (and probably would not stop you from purchasing it again, if you wanted to).
It's something that publishers will probably go to in order to rescue hardcover sales, if the ever-so-much more profitable agency model for ebooks gets shot down (as the courts in the US and EU are looking at it quite closely).