So I believe downloading is absolutely distribution - you become your own distributor to yourself.
Nope, the one that offers it to you is distributing. Whether that person is authorized to offer it to you is the issue, not whether or not you have the right to accept the offer. Nothing in copyright law that prevents you from accepting it or requiring you to check if they have the legal right to offer it before doing so.
If that were the case, everyone that bought that copy of Orwell's 1984 that Amazon deleted from Kindle devices would be guilty of infringement.
How could you ever know for sure if everything you buy or acquire is authorized to be sold or given away to you? How can you ever be sure that none of it is counterfeit or unauthorized?
You have to take the word of the merchant. There is no other way. You'd starve to death tracking down and waiting to hear back from all the copyright holders to find out if the images on the food packaging were not infringing on someone's copyrights.
And you can't just assume that everything free is infringement, because it's not. The RIAA labels themselves give away plenty of free stuff and have been for many years. I have stacks of CD's I have collected over the years that were given away for free at music stores, to promote lesser known artists, that were authorized by their labels.
And you can't just assume that all free digital files are infringement. What about sites like Last.fm that allow artists to upload their works and offer them to the public for download, free of charge?
Oh, that's different?
Well what if someone pretending to be the artist uploads it, unauthorized, and you download it? What if the artist sold the copyrights to it and then uploaded it? He would no longer be legally allowed to offer it to you. But how could you ever know that?
This is why the consumer is never punished for someone else's distribution. This is why there is nothing in the US copyright laws that allows punishing the consumer or end user.
There has never been a single case filed against a downloader in the entire history of copyright. They have only been sued for distribution, uploading, making it available to others.
You know whether or not you have the right to distribute something. Nobody else that accepts it from you really ever does.
And yes, you can legally save a copy of every copyrighted work you view online to your hard drive, as long as you don't distribute it to others without the permission of the copyright holder.