Agree mostly, but remember leader and manager are not synonymous and most managers are in fact not leaders at all. In fact less than 1% of people are truly leaders (per statistics in both Gallup and HBR).
Also, references are pretty meaningless now (except maybe client references) since most people just have a friend do it for them.
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Manager is a title. The term "leader" is an implication of obligation of status at a given workplace. A manger without "leadership" skills will underperform at a base level and fail to bring out the best in their employees hence promoting low productivity/poor work quality/higher stress levels/etc. As far as references go, you can have a friend try to "do it for you" but any manager worth their job will be able to realize that is the case after spending a few minutes actually following up on those references. Your numbers look great, but real time spent in a workplace dealing with these issues speaks volumes.