If you shot on DV or BetaSp, you wouldn’t tear off the cassette and just save the lose tape would you?
You shouldn’t do that to the BPAV either. All that stuff is metadata than many NLEs need to handle the files. You can’t through a pile of lose tape into a tape deck and expect it to play either.
Also as NLEs advance they make advances in playing back file based formats. CS5.5 handles this much better than CS3. CS5.5 handles the .mp4 files natively, although I’m not sure if they must use all the metadata. That alone would be fixable.
You can rebuild the metadata by importing the orphaned .mp4 in ClipBrowser 2.6. It can create new BPAV although the metadata won’t be the same, it will be usable. From there you may need to wrap to MXF for NLEs.
It would be wise to examine Sony’s site before making assumptions about workflow.
https://pro.sony.com/bbsc/video/related-recently_added/video-xdcam_ex_adobe_premiere_pro/
https://pro.sony.com/bbsccms/assets/files/micro/hdtapelessworkflow/brochures/25637_Adobe_Premiere_XDCAM_R1.pdf
Reading the manual for the camera and ClipBrowser is also helpful.