Clearly, costs include more than just money:
The free mobile phone requires a one-year contract. Obviously the cost of the phone is built into the monthly fee.
Waiting in line to get a free ticket to an event requires an opportunity cost (the value of your time while waiting), and therefore the ticket is not free.
Filling out a form to get a free white paper means the company now has your email address and perhaps other personal details. You have given the company something valuable so the white paper is not free.
Make it as close to free as possible
I offer a free ebook library with downloads at no cost and no registration is required. Even this has a (small) cost because it takes a second to click a link and maybe two are three seconds of wait time for the 1MB file to download on a high-speed connection (more on slower speeds). But this is quite close to free.
As you work on your content marketing plans, push back on those who misuse the word free.
My research shows that a totally free white paper offered with no registration form will generate as much as 50 times more downloads as the same white paper with a registration form.
Which would you rather have: One email? Or 50 people exposed to your ideas?