People can say anything they want about running shoes, and manufacturers too. It's 99% nonsense, not based on any evidence (example). There are basically only two conclusions I know of that are supported by evidence:
(1) If you're interested in reducing your chances of getting an injury such as a repetitive stress injury, the evidence shows that your likelihood of injury is very insensitive to what kind of shoe you use. The evidence only really shows that changing what you do (changing your shoes, changing your running style, ...) temporarily leads to a higher probability of injury. The interpretation is that your brain-body system adapts in very sophisticated ways. It can adapt to almost anything, but it can't do it suddenly.
(2) Having less weight on your foot increases performance.
I recognized that some surfaces (especially the gravel) trouble the mentioned shoes pretty much. I feel like the sole is too thin. So, what do I have to look for in "all terrain" running shoes?
The evidence ([1], [2]) does not support the idea that a thicker, more cushioned sole reduces injury. It appears that your body adapts to whatever amount of cushioning you have.
The way you pose the question is interesting, because it implies that you believe trail running to be more stressful than running on streets, so that more cushioning would be needed. Among many runners, the conventional wisdom is the opposite: they believe that hard pavement is harder on the body, and that they're less likely to be injured if they run on nice soft dirt and turf. Anyway, neither view is supported by the evidence.
As a runner, I always try to focus on the happy part of this message. The happy message is that no evidence forces you to do anything in particular in order to avoid injury. Therefore you can do whatever feels good and enjoyable, and not worry that you're going to get hurt because you're doing it wrong.
What to look for in (trail-)running shoes for various terrain?
Because there is zero evidence for essentially any of the manufacturers' claims, it's not a good idea to pay more than you have to. Buy cheap running shoes. If you're trying to run fast and competitively, buy lighter shoes. But do not suddenly switch from very heavily cushioned shoes to minimalist shoes, because the sudden switch may not allow your body to adapt quickly enough.
