Yes, a Blake stitched shoe only has a single sole (frequently thin) stitched directly through the upper and insole. A Blake/Rapid has a midsole that is around the thickness of a welt stitched on in the same way, and then a full outsole stitched to the midsole using a welt stitching machine. Since the midsole is a full size sole, it contributes more to the rigidity of the shoe, whereas a welt is only around the perimeter. Also, with the prevalence of fiberboard insoles that are used in Blake/Rapid shoes, that is a factor as well. The leather insoles that are used in Goodyear-welting are less rigid than fiberboard ones.
I said that they have insoles (see above). That said, insoles don't count when you are numbering the soles. Only outsoles count. Single, double, triple, etc., are only numbering the outsoles.