It would be an equivalent population who weren't asked to change their diets.
There are multiple reasons the patients in this study might not be comparable to participants in other studies or to the general population. Age, gender, average disease severity all need to be controlled for. And if nothing else the simple fact the patient knows they're being monitored could have an impact on all sorts of behaviors.
Yeah, these are interesting results, but without a control group you can't say for certain what is causing an effect or, actually, if an effect exists.
Which is actually an ethical quandary when you think about it. A doctor's ethics are really tested when he has to say to some patients "sure, I think you should change your diet and you'll probably die if you don't, but you're part of the control group!"
One more ethical (and still statistically somewhat interesting) way of administering such a study would be to bring in doctors advocating different sorts of diets. The Cleveland Clinic hasn't done such a thing but they probably could: they've got a group that advocates the rigid vegan diet and another that advocates the Mediterranean diet. Not as good as having a control group that continues to subsist on cheeseburgers and coke but it actually can test a few specific ideas, like the vegan claim.
You're right, of course. But whether a study is scientifically valid and whether it is ethical are two orthogonal questions. Similar concerns are why most cancer therapy trials end up looking more like A/B testing than classic experimental/control experiments. The point I was trying to make, though, is that you need at least two groups which differ only by a small set of (ideally one) known variables to draw any real conclusions
This is a very commonly known effect, which makes me more than a bit suspicious of this particular study.
This is also why a control group with random assignment is necessary, particularly in the social sciences. There are simply too many confounding factors to make epidemiology useful in basically any way.