Given a large number of trials, any random series will produce a large number of perverse-looking short streaks. If 100 people flip a coin 5 times, you should expect 6 of them to get the same result on every flip, but it will look strange to those 6 people. One-in-a-million chances happen all the time in a world of seven billion people. If millions of WoW players attack 100 times a day each, that is a lot of chances for long streaks of misses (and longer strings of hits).
More recently for me, it took two weeks to complete the Chasing Marcia achievement because one of the daily quests just did not appear for two weeks. What are the odds of that? Well, not bad. There are 5 quests, so 0.8^14=4.4% chance that any one quest will not appear for two weeks, but since there are five ways it could happen, there is a 22% chance. You should expect that to happen quite a few times each year, and if you started the dailies today, you should expect that 22% chance it will take you more than two weeks. (Maybe Blizzard does have some kind of streakbreaker in there, and maybe I just hallucinated having done the daily on a day I missed.)
I know all this and was just vaguely amused at the fishing streak. A similar thing contributed to my leaving The Lord of the Rings Online™ for about six months. I was trying to complete the Annuminas armor set, which involves getting the boss drop in each of three dungeons. With six fellowship members, that is a pretty clean 1/6 chance, minus the occasional member who just felt like running the dungeon but did not need that piece. In 16 tries, I won that 1/6 roll once. This should not be surprising: the expected value is to run each dungeon six times, and for everyone who wins a roll on the first time, there must be someone who just keeps running it and running it. I was not even up to 18 tries, and who knows, maybe it would have worked out perfectly and I would have won the next two. Independent probabilities, however, do not work that way: you still have a 1/6 chance, and I should expect another 12 tries to finish the set. And by that 16th trip, you get really sick of telling the new people to keep the silence-aura ghosts away from the healer.
Hence the approach of giving everyone a few badges, 1/6 the necessary token, or whatever.