When Lore is feeding Data negative emotions in Descent, Troi notes with surprise that she could "sense" emotions in him. Now, "sense" is a word that Troi only seems to use when referring to her half-Betazoid empathy, not general intuition. When she loses her powers, she says repeatedly that she cannot "sense" anyone, etc. This would seem to imply that she didn't just deduce that Data was experiencing emotions, from his behavior or something similar, she actually felt them empathically.
How is this possible? We know from a number of episodes that Betazoid telepathy, and therefore Troi's half-Betazoid empathy, are biological in nature. There's a specific part of the brain for it, and a neuro-chemical involved in its function. We even know that there are certain species on whom Betazoid telepathy doesn't even work, because their brain structure is too different.
So if a Ferengi's brain is too different to be read by a full-Betazoid, how can Data's not-even-a-brain be read by a half-Betazoid?