From my experience yesterday, I would like to say that I think the "Fish Counter" is quite buggy in that sometimes it works, other times it does not.
For example, this past weekend I was fishing in Azshara trying to complete "The One that didn't get away" (as awful as that achievement is). When I decided to take a break, my fish counter had gone from 500 to 590 catches. Later that night, when I logged back in and went to Dun Morogh instead (since I think the 15 lb Mud Snapper may be easier to catch - at least I CAUGHT several 10 & 12 lb Mud Snappers unlike my time in Azshara where I caught only 1 9 lb Lobster), my fish counter said I only had 500 catches! Furthermore, after catching several fish there (Raw Brilliant Smallfish & Raw Longjaw Mud Snappers mainly), my fish counter didn't move at all. After getting booted from the server (probably because I then went to go make dinner and didn't log out), I continued to fish in Dun Morogh and the same fish started to register on the fish counter.
Lesson from this Post: The Fishing Counter is buggy so make sure you're getting some fish that register before you rule them off as not counting as a fish.
(Besides, we'll all need to catch a zillion things in Dalaran anyways to achieve several achievements on the way to the "Salty" Title so an inaccurate fish counter here or there isn't really a big deal as long as they get it to work sometime.)