I don't think it is. I'd imagine it would be something like winning the two trophies at the start of his reign, before his slow slide into madness. It's not that people have an overriding memory that's completely bad, it's just that people thank him for the good times, but when faced with the proposition of taking him on again, they rightly remember the baffling moments and flaws that he had.
As said anyway, why are you acting like Rafa is the only option in World football? And why are you using him as a stick to beat Klopp with? This is more about the potential of Benitez being available, than any real sort of misgivings with Klopp. You're just jumping on the opportunity because we've fucked up in the Summer and Rafa has kept Newcastle's heads above water. It's myopic and typical Modo. Always got to have someone to hate if you've got a personal favourite in a similar role. See Hendo/Lucas, Gerrard/Lucas, Rafa/Klopp, Coutinho/Lallana, etc.
It's a retarded game.