I am pretty confident from my own experience that the study’s conclusion is broadly true. But the study leaves open one obvious alternative explanation: people who have enough free time to exercise regularly (and exercise was used as a stand-in for fitness level, it doesn’t look like they actually measured anything else) could have less stressful and anger-inducing lives overall.
Anecdotally, I started lifting again a few weeks ago. Took a few years off due to Covid complications, but was previously exercising regularly.
Walked up to the bar stressed about all sorts of things, everything is expensive, car is making weird chafing noises when I make sharp turns, politics, this and that.
Did 3 sets of 5 deadlifts with a 60kg bar. Barely any weight on the bar since I didn't want to annihilate my joints. Regardless, as I finished the sets, all that stress was just gone, and it stayed away for days. I was calmer, clearer, more present.
I don't think I have fewer reasons to be stressed since getting the gym membership, but I sure am less stressed.
Deadlifts in particular, but really any full body lifts have always been a mental state degauss button for me. Doesn't matter how many problems you have before you walk up to that bar, you'll barely remember them when you're done.
Not saying "cardiorespiratory fitness" and "heart rate" are 1:1, because they're certainly not, but beta blockers are a known treatment for certain kinds of anxiety. I can attest that taking low-dose propranolol twice a day (without pulling any other levers related to lifestyle, stress, etc.) has helped me mellow the fuck out, which I sorely needed lol. So I would wager that cardio fitness is itself correlated with anxiety and anger, although in practice it's tangled up with many other factors.
In addition to baseline heart rate, there's also some interesting stuff related to anxiety and heart rate variability. My understanding is that certain types of breathing exercises improve HRV in the short term, which is good for calming down if you're riled up, but people with good cardio health have a better baseline HRV in the first place. (Also, this has always been unintuitive to me, but higher variability is better for anxiety, not lower variability.)
Pretty much everything related to exercise is a direct or indirect positive effect for health.
Stress relief, tiredness leading to better sleep, physiological effects of muscle gain, physiological effects of weight loss, social interaction in shared spaces, exposure to sunlight, push to improve diet in pursuit of fitness goals, better self image, social effects of becoming more physically attractive…
Alternatively: People who spent their time regularly exercising instead of arguing on Facebook or X, have lower anger and anxiety.