Reading thesis on cone tracing, did the author make a mistake? I am reading this document that talks about signed distance field rendering.

In that document section 6.3, on the topic of cone tracing, it says:


  Cone tracing is an extension of the sphere tracing algorithm. In
  addition to the ray, a cone is created and expanded in the marching
  direction. At each sampling step, the current cone radius is compared
  with the minimum distance from the distance field. If the SDF value is
  smaller than the current radius, the cone has intersected an object
  [14]. This incurs very little additional cost to the normal sphere
  trace, while providing useful intersection information.


In particular: If the SDF value is smaller than the current radius, the cone has intersected an object.

Am I reading this wrong? there's no way that's true. Consider the following diagram:



From that diagram, it seems obvious that for any cone radius $R$ there exists an SDF value $\epsilon$ such that $R &gt; \epsilon$ and the cone doesn't intersect the sphere.

Am I interpreting the document wrong?
It’s kind of inaccurately stated—by comparing the SDF with a linearly increasing radius, the shape that’s being traced out is a cone with a hemisphere on the end, something like this:



At any point along the horizontal center line, if the distance to the nearest surface is less than the current test radius, the cone-plus-hemisphere has intersected that surface.