The term "nuclear waste" encompasses more things than just spent fuel. Tools, containers, reactor linings, etc; these things become radioactive when exposed to the primary radiation source.
But, of course, those are not the high level wastes that need the sort of super secure containment that Yucca Mt represents. Reprocessing is the best solution to the waste problem. Right now volume is our biggest issue and thanks to our over-broad interpretation of proliferation treaties we are all but ignoring this solution.