In the wild tree squirrels dig up bulbs, onion like forms with layers, 'corms', some of which are edible, yet others are toxic.
As to whether all the humanly edible allium family sources are toxic or non toxic to rats and tree squirrels, I haven't as yet found this confirmed or denied, though not saying it hasn't been.
I have seen squirrels take a nibble on toxic mushrooms (before I had a chance to remove them from my yard); yet no doubt they did for they left teeth marks in the tops (generally one or two small tasting bites). Generally speaking, it is mushrooms that are extreme in pH that are toxic, but then again other compounds found in some mushrooms are toxic due to other than their pH value. And though they recognize a high alkaloid by taste, and a highly acidic (very high in oxalic acid), they are known to eat toxic mushroom at times, and as a result some die, where others do not; this 'perhaps' from only tasting it?
As the following article explains, most often this is do to the dose consumed. For this reason I wouldn't support giving a squirrel a toxic or semi toxic mushroom to eat, and the same with corms, even if edible to humans. Not all allium plants are corms (bulbs with onion like with layers).
The ancient Greek Paracelsus is accredited with this saying:
"All things are poison; the dose makes the poison.
https://en.wikipedia.org/wiki/The_dose_makes_the_poison