Illusory existence is the Buddha-nature?
At least in Mahayana Buddhism there is nothing between its covers to suggest that absolute substance or tathata (sometimes translated as suchness) shares its throne with phenomena; that somehow a phenomenalization or configuration of tathata is just as important as tathata, itself. (This holds true for pure Mind as well which is interchangeable with tathata.)
Dethroning phenomena might be rejected by those bound down to phenomena who have failed to catch a glimpse of tathata or pure Mind to know otherwise. However, in an argument they might be forced to concede that there is at least a spiritual distinction to be drawn between tathata and its configurations, the latter being thoroughly empty (shunya). This is what Nagarjuna and those of his era tried to do, that is, show those who cannot let go of phenomena, that they really have no sound basis for their arguments that can justify phenomena-clinging. Their world is a fiction as are their ideas of causation, etc.
This sort of gets turned around sometime later when Buddhist scholars, especially in Japan, assert that phenomena are the Buddha-nature or the same, illusory, mundane existence is the Buddha-nature. Dogen, for example, goes so far as to declare, "Seeing the Buddha-nature is seeing a donkey's jowls or a horse's mouth." Such an idea, however, is nowhere to be found in the Buddhist canon. It is a mistaken interpretation, one that no Indian Buddhist like Nagarjuna would ever make. Such a mistake leads to duality. The grasper of illusory existence creates duality by his blindness and ignorance of the true nature of reality: the way things really, really are.
From the perspective of tathata, there is no thing like a donkey or a horse certainly not their jowls or mouth! In truth, nothing exists except absolute reality. But this is almost impossible to actually realize for the average person or Buddhist worldling/prithagjana. Yes , if they wish they can give it lip service or hold this idea to be dear. But this is almost like hoping to cross to the other shore while forgetting to enter the ship bound for it.
