The TV series changes a few things - adds characters and other SF elements. However, the essential core of the series is similar to the movie and true to the spirit of the original novel, so I would count that as a "reimagining" that works. I still prefer the original, mind you. But I love the movie and don't hate the TV series.
Um... okay. Then you don't have any inherent problem with reboots? I guess we agree then. If that's the case, how does that square up with your previous point (unless I was reading it wrong) that if a Star Trek writer wants to use Kirk and Spock, then he should just create his own characters and his own universe -- a point I'm still not grasping.