I'd expect high intensity training to have a detrimental effect on sperm quality. Sperm are made of protein(s) and hours of high intensity training will divert a lot of protein towards muscle/tissue regeneration. The human body is pretty good at shuffling resources around, especially from non-essential subsystems. Sperm only live for 10 days anyway, so the body is constantly recreating them. Heat is also bad for sperm, even 37oC body heat, which is why the testes are not completely internal. So while it may not be good for your current stock, or next 10 days worth, a month off the bike should be back to normal. I'd be very surprised if cycling lots did anything to damage the mechanisms for creating new healthy sperm, and certainly nothing at the genetic level.
Why cycling in particular (given it was a test of triathletes)? Probably because it's easier to do long stints of high intensity training on a bike. Try going for a nice 5 hour "zone 3" swim or run.
The article is a bit misleading, not surprising since it's just tarted up agency copy (googling for the quotes gives hundreds of similar articles on other news sites). It starts off by quoting "less than 4% normal looking sperm", which sounds bad until you find out that "normal" is only 15-20%. The final paragraphs of the article are just speculation. One small study found reduced "normal looking" sperm, other studies had "mixed" results. There's also the: "He added that 40 years ago cycling was much more common but there is no evidence men then were less fertile." quote.
Maybe I'm just grumpy with it as I've been reading Ben Goldacre's Bad Science which does a pretty thorough job of ripping to pieces most journalistic reporting of any scientific issues.