My guess is that "veteran" has to be taken in context of the conversation. For example, in [this conversation][1] "verteran" presumedy would  refer to users with both 3K + reputation and experience in reviewing close votes on SE.

Short answer - verteran implies not only reputation, but also some experience with the topic at hand. 
  
You might also find the [privileges][2] page useful.

  [1]: http://meta.askubuntu.com/questions/11592/how-can-we-encourage-3k-users-to-review-more-close-votes
  [2]: https://askubuntu.com/help/privileges