No. This study is confounded and provides no evidence of anything. The problem is that people's willingness to exercise depends on their health as much as or more than their health is affected by exercise. Because this study did not involve an intervention (it just pooled a bunch of surveys), it can't distinguish between exercise causing reduced cancer risk, or a third variable affecting both.
I will add that this is the sort of thing that peer review theoretically ought to stop, or at least force authors to include caveats for. Unfortunately, studies with this sort of methodology make up most of the so-called studies published, so they can't really do that.
The problem is the press representation of the papers as something they're not.
These types of papers should be published, because they are necessary to decide which hypotheses to test with interventional studies.