Would ray tracing not be a form of distance based intersection testing though?
Not necessarily. You can have a ray-object algorithm returning just TRUE-FALSE for culling, and a separate ray-object algorithm returning data needed.
However, multiple ray-casting can still lead to missed hits. A "swept volume" method, perhaps using bounding volumes in broad-phase, would likely provide more consistent results.
When used for broad-phase culling, that method can be implemented as a TRUE-FALSE test (faster). Then iterate through the list of hits using a more refined test, calculating the parameters you need (such as distance, hitpoint, surface normals, etc.), and perhaps using more refined shapes for the test - again, depending on what data you need.