While I have little doubt in the conclusions of this study, since it was performed by well-qualified researchers and published in a respected, peer-reviewed academic journal, it's important to understand the findings are simply the reported results of this (single) study.
Let me get right to the point: this research DOES NOT mean that exercise programs for firefighters are dangerous, unhealthy, or should be discontinued!
Although it is definitely valuable in contributing to our overall body of knowledge about firefighter health and safety, the results of this study are necessarily limited and must be considered in context.
The benefits of regular exercise are well-established in numerous studies, for both the general population and firefighters.
With heart attacks still the leading cause of firefighter fatalities each year, there is no question that fire departments must continue to emphasize physical fitness as part of an overall health and wellness program that also includes annual medical exams, a nutritional component, and behavioral health counseling...among other things.
What this study should absolutely cause us to consider is the type of exercise(s) we support, allow, encourage, or mandate.
It may seem obvious, but all "exercise" is not created equal; if you go to the fire station, don't warm up properly, and start doing 1-rep max effort Olympic barbell deadlifts you are going to hurt yourself, period!
Same thing if you decide to train for a marathon by starting out, cold, with a 10-mile run.
Be sure to enlist qualified professionals in designing your physical fitness program, make sure you are medically cleared, and — as this study also suggests — pay attention to the results. If you're getting injuries, then change the program; but don't stop exercising!