Allow me to shed my opinion here:
You're BOTH (all?) right...
First, free:paid isn't the only term sponsors call ratios. click:free and click:paid are some other commonly used ones.
In this case, minimum is a much more often-used term (I've never seen anyone call it a free:day ratio myself), BUT free:day is a ratio like any other.
Just because it's not used by the masses doesn't make it wrong
In any case, you're all right so..........I'm off to the office now.
Alex is right though, in the case of our promo, we had NO ratio/minimum of any kinds to get the payout...because, it was a promotion.