The reason that mileage is a poor denominator (as stated above by someone else) is that it is too difficult to determine. I concur that bike registrations are a somewhat better, if imperfect means of assessing CHANGES in risk, though not absolute risk. And by that criteria the risk assessment is not nearly so horrific.
It's a bit like assessing airplane flight risk. It turns out that the majority of crashes occur during take-off and landing, not in-flight, thus many have criticized using flight miles in the equation. I have read that using number of flights as their denominator results in a five fold increase in flight death risk and is more accurate in terms of assessment compared to other modes of travel.
I think a lot of people have made good points. Clearly, regardless of whether or not the risks have changed a little or a lot, riding a bike is inherently dangerous. Similarly, we should always be doing everything we can to make it safer (education, licensing requirements, better gear, safer bikes, car driver training, etc., etc.) no matter what the trends are.
I think an important point is that this article was not written to promote a renewed agenda to improve motorcycle safety but to sell papers with another gloom and doom, bikers are wackos, grab the kids and get them inside, orientation. And it worked, as every person I spoke with who doesn't ride, commented to me how insane it was to ride a bike.
In Tucson, this ran as the front page lead article - meaning the editors were calling this the most important news story in the world for that day. I'm sure it helped sell papers to their target population, a demographic not composed of a lot of riders.