I think they meant, for humans, the dose makes the poison. We would have to eat a very large amount of warfarin to have trouble. Rats get hurt from a small amount.
Poison is dose dependent, but the actual dose dependency is different between species.
Some birds have incredible metabolic rates --> take for example a humming bird.
However if I were to assume a canary has twice the human metabolic rate, it isn't a very good sensor. So, the canary dies half as soon? But the canary isn't even about poisonous gas. I believe it's about explosive methane gas, as their gas lanterns would need to be extinguished if the canary died, or else the gas leak that killed the canary could explode.
So, yeah, anyway. I think your information on this example is wrong, please feel free to correct me
Since they can't throw up or burp, something that produces enough gas (More than a regular soda) could in theory kill a rat, but just make a human slightly inconvenienced, or on the same idea, you could wrap the poisson on an emetic agent to make it safer while not affecting the rat at all