Totally wrong. You still have to get to the final and do what you have to do to gain those trophies. If he wasn't any good they likely wouldn't have got that far. If they weren't a great side then it's an even bigger achievement.
Nobody is suggesting they're major trophies, but it's about having a winning mentality, that's the point that everybody is missing.
As for Leicester they are a big club compared to many (they were big enough to win the Premier League title), and they were in total disarray when he took over. He cleared out the deadwood and many thought he had made a mistake but he got them promoted with 97 points.