Steve, I understand what you are saying, but if a physical object exists, then it should be detectable by physical means. However, it has not been detected in the radius of a few light years, whereas modern astronomic instruments can detect stars distant billions of light-years.
That's why it seems so implausible to me that the sun dual exists. The sun's old dual seems to exist, but it has escaped the gravitational constraint so much time ago, much before humanity existed.
Please note that a hint of doubt is present even in Cruttenden's site, as I emphasized in the following sentence:
We believe that this approach of analyzing the precession observable (the sun’s motion relative to the fixed stars as seen from earth) will provide valuable and helpful data regarding the sun’s most likely stellar companion (if one exists).
The sentence is in the section 'introduction' of the BRI site:
https://binaryresearchinstitute.org/bri/introduction/binary-companion-theory/
