The common usage of the word "free" is something like "without cost" (yours doesn't work and I actually couldn't find a definition that explicitly says "money"). Placing ads in an app has various costs, just not usually monetary. I don't think you need to redefine anything or go to this odd extreme you're trying to straw-man into the argument.

"There's no such thing as a free lunch" agrees with you - things described as free often have some cost, even if not monetary