> Is this just word lawyering over what "subsidize" means?
Insofar as words have meaning, possibly. Before arguing that one group is subsidizing another, you'd first have to argue that one group is being subsidized. Leaving aside the original meanings (which only describe public funds in the first place, which this isn't), and interpreting the apparent meaning, the claim is apparently that credit cards lose money on rewards programs for rich customers, and those programs are thus subsidized, and specifically that they're subsidized by poor customers. If that were the case, they wouldn't have those rewards programs. (I'm not claiming that no company in the world has ever spent marketing money they didn't have to or spent it unwisely; I am claiming that an absurd amount of analysis has gone into the finances of rewards programs, in particular, and it is extremely unlikely that card companies are spending more to acquire a class of customers than the revenue they get from that class of customers.)
Now, more broadly, if you want to claim that credit card companies make more money from poor customers than rich customers, that would not be too surprising of a claim. (It's not obvious if the evidence supports that, and it seems like it may not be the case, but let's set that aside for a moment.) That's not a subsidy, and I wouldn't even call it "regressive", any more than I'd call a company that makes more money from rich people than poor people "progressive".
If you want to say that, in general, the practices of credit card companies and the financial industry are not fair to lower-income people, I would agree with you there. I don't think any subsidizing is going on, and I don't think rewards programs are a redistribution program; any such claim would imply taking a loss on a class of customers but keeping those customers anyway. But I absolutely would support a claim that (for instance) credit cards are predatory. Or, for instance, that airline miles programs are deliberately confusing and misleading and to a first approximation no customer "makes money" on those either.