Eh it's more tricky than that. With many enlisted when someone says they are a Ranger they assume as in actually a part of a Ranger battalion rather than just having a Ranger tab. It's a notable distinction but not enough where I would use it as a attack on Cotton.
I respect you as a poster but I think you have it exactly backwards. Cotton is telling a lie that passes as true on a specious technicality, not the other way around. Not picking on Cotton here, either, this is a very common thing among politicians of all stripes... stretch the truth as much as you can plausibly get away with it.
Why would they lie about stuff like this. There are records. I say they because Blumenthal did something similar.