How many of those 10k purchases didn’t buy it because it was available for free somewhere? The point is, as you said, you don’t know.. However we do know the opposite is true, once Napster went away people started paying for Pandora. Netflix password crackdown lead to increased subscriptions.
When your desirable product isn’t available for free, people will trend towards buying it.
I often download books before buying them because I otherwise have no reasonable means to judge their content. This is not much different from flipping through the pages of a book in a library before buying it. The appeal of reading from an actual physical book is not something that any digital form can replace, so the book being available in digital form won't stop me from buying a copy. I also have no interest in Kindles and DRM.
Music, on the other hand, might be a different story except for select audiophiles who prefer vinyl.
So I don't think we can generalize to "product" like you do in your argument. Details and facts actually matter.
Corey Doctorow has the right idea. <sic> “I give my works away for free. Every time I gain another fan I gain another person who might want to own the hardback of my new book.”
If your desirable product is available for free more people find you, like you, follow you, patronize you. A lot of those people have money and are happy to give it to you to support you continuing to make good work.
This distribution problem doesn't really exist with books at the moment as Kindle exists.