Full scholarships at the Di-DII level are very rare, indeed, and they are almost always pitchers.
Full rides -- scholarships plus financial aid (academic, fed. and/or state grants) -- are relatively rare, too, because most financial aid packages contain student loans. Full rides, though, do happen.
A lot of parents say their kid has a full ride if they're not paying, even though he's got loans. And I suppose, though not totally accurate, it's not wrong, either.