What they are basically saying is that viruses can use the Bitcoin blockchain to communicate with their authors. So for example the virus author could put code into the blockchain and the infected computers would all get that code from the blockchain and run it.
And that's a legitimate concern with any method of communicating over the internet.. whether you're using the blockchain, a centralized server, some other P2P mechanism like BitTorrent or (as you mentioned) even something like PasteBin. Theoretically a virus, trojan or other malware could just as easily use a GMail account for the same purpose. Any of those methods would probably be a lot easier and less expensive for the malware author than repeatedly paying to put messages in the Bitcoin blockchain (either as fake outputs or OP_RETURNs), but I can see how putting the messages in the blockchain would be much more resilient than most of the other methods I can think of.
Most people are going to read this article and take it to mean that computers can be infected via the blockchain. This is not true. What they are talking about is using the blockchain as a way for hackers to send instructions to infected computers.
Perhaps it's the way the article is written, then? I took to mean the same thing, especially since it specifically mentions "fetching information from transaction records and running it as code" and in that light it's nothing but FUD, no Bitcoin client does that and there's no need for any Bitcoin client to ever do that. Of course some hacker using it to send messages to control infected computers is a much more legitimate concern. Even worse, I'd think, would be a hacker using it to send messages
from infected computers back to himself. But we already have viruses and keyloggers that do a pretty good job of phoning home without ever having to touch the blockchain.
