I think it's important to know other musicians' influences. It helps us understand where this particular artist is coming from, where he/she gets ideas and such. As a musician, it's an essential part of research.
For example, when I was checking out Matt Cameron during my younger years, I discovered through his Modern Drummer interview that he was highly influenced by the likes of Steve Gadd, Tony Williams, and other great jazz drummers. This made me curious; and thanks to that, that's how I discovered master drummers such as Gadd and Williams.
Another example... I admire John Bonham so much because no matter how heavy his drumming is, his groove still feels oh so good! Later on, I discovered that Bonzo is highly influenced by Motown music. And so I figured, that's where he got that great sense of feel and groove.
I can lay down more examples... It's great that music stuff is being passed on from generation to generation. And it's great that we have the opportunity to look back, do our research, and appreciate how music and drumming evolved over the years. And we ourselves can share and pass amongst each other the knowledge, insights, learnings and know-how.
Before I judge a certain musician, I find a way to know who his/her influences are. In that way, I'll get to understand them more as artists and persons.