If you want to inspect intermediate levels of refinement or other details about individual patches, then the Bfr interface is not a good choice for your task. Bfr does not apply adaptive refinement the same way as Far and there is nothing in a Bfr::Surface that can be inspected to provide information about intermediate levels. So you are better off working with the PatchTable and the TopologyRefiner as originally posed.
It appears the recommendation of Bfr above assumed that the "source points" you are referring to are the original control points of the mesh. But on rereading your request, it sounds like you want the source points for individual patches of the PatchTable at the same level of refinement.
The set of source points (a subset of the refined points) that contribute to the control points of a patch are not stored explicitly in the PatchTable, so there is no way to retrieve it directly.
You are correct in that you can determine the set of source points by inspecting the local point StencilTable. For each control point of a patch, its entry in the local point StencilTable identifies the source points from which it was derived. So you can gather the entire set of source points for the patch by inspecting stencils for all control points of the patch. But that will include the P5 neighborhood (from the diagram you cite) and you will not get any ordering information from the stencils.
There are other possibilities, but they are far more convoluted, so I am reluctant to suggest them at this point.