I think their point is valid, i.e. the same stress on SOME muscles, however on trails there are many more muscles in use than on flat. Which means that the overall stress is greater on those fewer taken in use on flats. So overall, I vote trail is more preventive for overuse injuries.
At the same time though, I also believe the body adapts greatly to whatever surface but the argument "asphalt feels harder on my joints" is not valid. This is the difference between many arguments around here, which is seen in all topics, e.g. the vaccination thread. I don't think I'm biting over to much when claiming there are many flawed arguments around here.
We've seen more studies recently pointing in the same direction as this, namely studies showing that maximalistic shoes are more preventive for injuries. However, there is a big difference in feel and you'll feel like your legs are more beaten up after a run in flats than maximalistic shoes.
Saying all of this, I would suggest that experience and anectodes from you runners are valid points . As I can see, there are arguments in both directions, maybe showing that we have different biomechanics! Of course many claim that fall injuries and ancle sprain is more often recurring on trails and this is true, but the study did not look at that aspect.
For a long time, I have myself thought that running less on asphalt reduced my injury risk. Recently I have only been running on asphalt and I haven't had any injury so maybe my guess was wrong? Over my running life I've had many theories about many things, I've often changed my mind - often completely and I would say that I am more unsure than ever! More experience and knowledge have only lead me to think I know less. Tbh, I may not know the correct answers but this has been my take on this issue.