The point is to have an early warning in a situation where gas concentration potentially increases from harmless to dangerous levels, as in a mine shaft, where ventilation is limited. Something that is harmful in low doses to a bird isn't necessarily so to us, until it is too late, which makes the bird useful as an early warning signaller so people can get out early when the dose is still harmless and thus not easily detectable.
Thus the saying "the dose makes the poison".
Caffeine overdoses are too common among people and I've known friends that have died or almost died from them. (I'm strongly on the never side for caffeine pill usage as the risk of an OD from coffee is much lower and involves a lot more liquid sitting on your bladder.)
Theobromine in chocolate (and tea and other places) is a Caffeine relative that in us humans has a 1/10th to 1/100th the efficacy on our caffeine receptors. In dogs that relationship is reversed and theobromine is their caffeine and death by chocolate is their caffeine overdose.
People can overdose on theobromine too, it just takes much higher quantities still than caffeine.
Which yes, aligns with your point that doses matter, but the other thing useful thing to note about the Theobromine/Caffeine relationship is that subtly different but related chemicals have wildly different effects on different metabolisms. It's not just dose that matters, but also exploring the repercussions of entire families of chemicals (and the products they break down into) because you also need to know if a "cousin" chemical has larger efficacy at lower doses in people. (Results on small animals are still an early warning sign, the directions they may warn about aren't just exposure time or dosage amount, but also related chemicals and receptor paths and many other things.)