I've been having the exact same luck with dummy badges. I don't believe that the badges with free turns on them actually exist. They're just a mythical creature, like bigfoot or Steven Seagal, and people who claim to have seen them are really just trying to enforce the myth for tourist reasons.
On the other hand, I cleared the Splatoon machine with all the camera/miimaker/eshop/etc splat icons in it with that one free turn it gives you...Though it's pretty much only because the machine bugged the **** out. One of them just straight up fell through the stand it was on like it wasn't there.
Since I didn't really 'deserve' those badges, I'm now waiting for the Rabbit to ask me for money before he breaks my kneecaps.