Uh, no. It doesn't work that way. The fee paid to sharing sites gives you simultaneous, faster downloads and it stays with the site owners. It doesn't pay for the author's work in creating the book. It's as though the author said, "I just sweated bullets for nine months over this novel, but I don't value my skills and my effort. You can have it for free. Go ahead, it's okay."
Of course authors value their work. So do artists and musicians and plumbers. Try explaining to the plumber that you want to pay him once to visit your home and then share his services with twenty neighbors for free. If your plumber is the type with a colorful vocabulary, your answer will be a bright rainbow.
There is the issue that some people say books are overpriced, and in frustration think they should have free access to anything that can be put on the Internet. At least I can see where this attitude might come from. My response is to push the issue with publishers if you feel that way, but recognize that the author's portion you're paying when you buy a book is small.
A typical paperback priced at $7.99 might produce $0.64 for the author for each sale. If the book has 300 pages, you're paying two-hundreths of a cent to read each page. Cheap enough to not only enjoy your established, favorite authors but to try new-to-you ones every now and then. If you had to stand face-to-face with the author and count out two quarters, one dime, and four pennies and hand them over, you'd probably feel it was a good deal. But the Internet depersonalizes the experience and makes it easier to take the author out of the equation.
We can do away with the myth that all authors are rich and don't need their $.64 per paperback. Granted, a small percentage of writers are rich, but most of them got that way by moving up through the ranks (or they started out well off in the first place). The huge percentage of writers remaining (like the 99% of Americans) are dependent on that $.64 for all the costs of living and raising a family.
Enough ranting! I made a badge that I put on my blog to express my views of piracy. Here it is below. If you feel as I do, please help to spread the word. I bought the skunk graphic, but I added the noxious little cloud of gas behind him. ;-) The badge gets its point across in kind of a cute way. Copy the HTML code below the badge and insert it wherever you'd like the badge to appear.