Well, my ex worked on a rat movie that had almost 100 real rats (supposedly “trained”*) and there were pretty strict rules about how long they could work, what they could do as far as safety etc.
For example there was a scene in which thousands of rats burst out of drainage pipes into… a swimming pool of children! Oo, eek, the horror, the horror. CGI of course, was used for the “big stuff”, but for the close-ups of little rat legs paddling away as they swam (they were actually really cute)…
The pool had to be drained because they weren’t allowed in chlorinated water. The water temperature had to be very specific so the rats wouldn’t catch cold. Crew members had to stand in the pool in case some rat got a cramp and couldn’t keep swimming (and you got coated in rat crap for your efforts). After the swimming scene they had to go back to the rat trailer (which was also kept at a specific, rat-friendly temperature) to be dried off. Etc., etc…
Basically they were treated better than your average B-list actor.
This is in stark contrast to the chimps used in Project X in which there were serious allegations of beatings.
Some animals also suffer a great deal from the stresses of handling, transportation, bright lights, loud noises, being in truly weird and unfamiliar environments. So there is great care in making sure that the animals don’t undergo any trauma (like cold swimming pool water).
The disclaimer usually means they were following some pretty stringent guidelines, and or had monitors on set and/or vets on set and great care was taken to meet the animals’ needs. Approved animal wranglers also take great care to ensure the animals are safe. Kind of like having a gun wrangler on set to make sure all the phony firearms are used safely, the animal wrangler supplies the critters, but also takes on the responsibility of being sure the animal’s safety needs are being met.
I’m not sure how far down the food chain it goes. The TV show Fear Factor regularly has contestants eating worms and bugs alive. On the other hand , some movie that had huge bunches of cockroaches had a “roach wrangler”. So I dunno.
*Oh and as for “trained”… the rats just ran around and ate peanut butter that was smeared on the set. (CGI was used to make it look like thousands of rats eating peanut butter). When about 30 of them were supposed to run down a tunnel, only about 9 ran toward the rat-snack rewards at the end of the tunnel. The other 21 took off in every which way, climbing on film equipment, and leading the crew on a merry chase… A lot more CGI was used than initially planned. Lousy actors those rats. Just don’t follow direction well.