It’s funny, I sent a question to RIRRC yesterday and this is what they sent me this morning:

Hi, thanks for reaching out and great question! This can certainly be a bit confusing. Wet-strength cardboard is either made of fibers held together by a binding compound to repel water (frozen food boxes, kitty litter boxes, etc.) or the cardboard itself is lined with plastic (such as coffee cups). Fiber recycler add water to re pulp the fiber, so when the fibers are designed to repel water they don't break down in the re pulping process making them not recyclable through this process. Cartons on the other hand are constructed using a layering system. Some are a layering system of wax-paper-wax (like a milk carton) and other are a layering system of paper-plastic-aluminum-plastic-paper (like broth cartons). The buyer is able to separate our the good fibers from the other materials and recycle those good fibers. We hope this helps provide a bit more clarity to the topic!

There’s a reason for why they do what they do, just follow the rules and if you’re not just sure ask them. It’s not a big deal. Should it be easier? Absolutely. No doubt about it. But it’s not for right now, and for whatever reason you’re assuming that just because something SAYS it’s recyclable means it is, it isn’t. I don’t know how else to tell you that, it’s just marketing/greenwashing. Everyone needs to listen to their local recycling company since they’re who dictates what they can and can’t recycle, and I’m sure in the future things will change but it’s been like this for 10+ years here so nobody really has an excuse to not “get it” yet.