If they'd picked on Justin Bieber, then we would probably be asking why they didn't pick on Nickelback instead.
Why did they pick anybody to pick on in the first place? That's easy: publicity. It got people talking about their product.
Why do people in general pick on Justin Bieber or Nickelback? I don't really know. If I had to guess, I'd say that people dislike successful celebrities or musicians who they think have undeserved praise or success. That "undeserved" is of course highly subjective. Most people who dislike Justin Bieber are likely not in his target audience. Since his target audience is fairly narrow, you have a reasonably large pool of people to get onto your "Justin Bieber memes train".
It probably works the other way around too. Mention "Rush" and "rock and roll hall of fame" in the same comment on Reddit and see what happens.
On the other hand, many of the complaints leveled at Rush and Nickelback by critics are the same. Both have been called formulaic and repetitive (I don't agree with that, but I have heard it). So what is the difference between Nickelback, who get internet hate, and Rush, who get internet praise? I don't know. The obvious answer might be that Geddy Lee and Neil Peart in particular are both widely recognized as being extremely technically talented musicians, giving Rush something that other formulaic bands cannot fall back on... but I don't think that is a satisfactory explanation.
This article isn't really on HN because people want to discuss the merits of an internet meme about Nickelback. The origin/merit of the meme is rather incidental.