Little late to the party here, but maybe someone will scroll this far down and read this...
There are tons of problems with epidemiological studies like this one, and they've been discussed everywhere, including paleohacks. So I'm not going to spend too much time rehashing it, but I want to point out a couple of things:
1 - do you know what they classify as "processed meats"? If you're a researcher doing this study, you have to take everything a person eats and break it up into the predefined categories you want to study. Do you break it up by mass, volume, calories? Well, there's a study from the UK that says processed meats cause cancer (maybe it's the one you linked too or another one, I don't know I didn't read this one) and they took ALL of the calories from a slice of pizza and said that it's a "processed meat" if it has pepperoni on it. So unless you read the actual paper and talked to the researchers you don't even know how the foods are classified.
2 - When you do an epidemiological study, you're going "hunting" for correlations. And that's not science. You can hunt for correlations to start your study, to help direct the research, but you should NEVER use them for actual results. Here's why: when you look for a correlation between two variables, you have to pick some level of "confidence" that the correlation is actually a correlation and not just there "by chance". The standard in science is usually p=0.05 (or p=0.95 depending on whether you're coming from mathematics or statistics). What that means is that there's a probability of 5% that your correlation is "by chance" and not actually there. That sounds pretty good, but 5% is 1 in 20. So when you have a huge table of numbers from n epidemiological study and you take every pair of columns and look for a correlation you can easily run across some that are there "by chance". And since the non-correlations aren't reported, you don't know how much they tried to find something that is "significant" and it could be by chance. Here's my favorite cartoon that show this phenomenon: http://xkcd.com/882/
Just like we should always say "correlation does not equal causation" we also need to say "epidemiological studies are only good at best to generate a hypothesis"