I did not see where the article talked about downloading "paid" applications without "paying". What I saw addressed was downloading from non-Apple sites applications that could run on I-phones, from Google site those that could run on an Android or a Kindle. You may still have to pay for the download from the other site. The point was you are not restricted to one site for apps to run on your device. I suspect if I have a rooted Kindle, I could download from the B&N site where I would not be able if it was "unrooted" - but I still would have to pay B&N (unless it was a freebie).
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