I just ran a number of experiments using different MIDI styles and each and every style correctly played and notated Cdim, Cdim7, and Cm7b5. I inputted the chords as Cdim, Cdim7, and Cm7b5. So it appears as the chords are correct on the MIDI side of BiaB.

I surmise that on the RT side what you get is what the performer played. I have played a dim7 chord in place of the sheet music's dim chord many times, as long as it doesn't interfere with the melody.

Note that I have never seen a dim5 anywhere, but that may be because I input all of my chords myself. YMMV

Unclear if the pianist is a total beginner or a professional jazz player?

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware