Now if you put that glossy paper in upside down so it printed on the RC backing, yeah, it might leave some ink but even that usually doesn’t mess the printer up that bad.
Slightly OT, but I experienced just that recently.
Printing from LR with a particular profile the margins weren't as I had specified, and I couldn't find where I had some setting wrong. So I tried a different profile and made another print on the back side of the original bad print. The result was a black, gooey mess on the print. Out of curiosity, I kept the print around for three weeks and the ink hadn't completely dried!
That was my first time intentionally printing on the wrong side, and it was quite interesting. But as messy as the print was, the printer was just fine (P800.)