If there's one thing I've learned over my years, it's that there is no such thing as a consensus amongst any clubs' fans about anything. I didn't feel what you describe as a consensus and I don't remember it being even a significant minority position amongst the fans I know, online or offline. I think we're pretty pound that only one club has won the League Cup more times than us. You can describe that as arrogance if you like, but it is a simple statement of fact.
What I do remember is after Blues won the cup, someone posted on here a selection of quotes from one of the nose sites from the year before calling the League Cup "mickey mouse" because we were in the final. I think a lot of Villa fans enjoyed reminding them of what they called it.