Under the book’s reasoning, analysing «بِشْرٍ» as badal invites the repeated-governor test. Replacing «الْبَكْرِيِّ» would yield a construction like التَّارِكِ بِشْرٍ, which is problematic under the author’s treatment of the active participle and its complement here.
The book therefore treats «بِشْرٍ» as ʿaṭf al-bayān. This is a focused grammatical argument, not a ban on the overlap of the two categories in all examples.