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Shit like this is why I am always on my guard against offers of "free" anything from corpos. Always.
(i.imgur.com)
Sometimes they even get rubes to pay for the privilege of being exploited and sold off in marketable pieces, such as 23andMe. 
I hate this saying because foss stuff (like lemmy) is also free, plus there's no guarantee that your data doesn't get harvested when you're a paid user in proprietary apps
Regarding the second point, conditionals don't work like that in a formal sense, they are expressing a sufficient rather than a necessary condition. A -> B can allow you to deduce B from A, and implies ~B -> ~A, but that all does not mean that you can derive A from B, i.e. it does not mean B -> A.
Put more legibly, you can be the product even when it isn't free, but if it is free, you can be sure you are the product.
Pushing my shoehorning of formal logic even further, this inference should be understood as being within the "domain of discourse" of things offered by private companies. Air is free, but that does not somehow make you a product. Your neighbor might do something nice for you out of the kindness of their heart, that does not make you a product. If Walmart wants to give you something, it's because they want to sell you.