I think we should be clear..
Solanine is in Potatoes not Tomatoes
Tomatine is in Tomatoes, not Potatoes.
Both are glycoalkaloids and each is different in effect.
With both plants, all of the parts bear their respective poisons. That would include the white part of the tuber and red part of the fruit. Now, solanine is quite prevelant in the leaves of potato and can cause illness. Tomatine is also found in the leaves of tomato, and to date has not caused any reported illness in humans.
Concentration, as with many poisons, is the real question. Consider, 7 drops of bleach in a gallon of water is a high enough concentration to kill microbes, but has barely any effect on humans and animals. Consider, a TRACE amount of arsenic is required for humans to live. Carbon Monoxide is required for human (and other mammals) bodies to function. Of course none of these can be tolerated in high concentrations.
Not many potato leaves are needed to get a high concentration of solanine. On the other hand, the needed amount of tomato leaves to get a high enough concentration is exorbitant. I have cooked with tomato leaves for many years. The leaves are a key ingredient to my spaghetti sauce.
Dosiedoe (as well as the wild rabbits, argh!) enjoys tomato leaves. There is at least one other member of this forum who feeds her rabbits tomato leaves regularly.
I don't mean to belittle anyone's adverse experiences with tomato plants. But empirical evidence as well as nutritional science would not support a categorical claim of "deadly" for tomatoes.