When undergoing a Boarding Operation, owned ships participating on the boarding op will still fire at "harmless" surface elements such as shields. They will keep firing on them, bringing the hull way below of the threshold you set, and may cause it's destruction. This also happens when setting the behavior of ships to "Target Turrets" only.
Other issue is that once the surface elements are destroyed, the Owned ships Turrets will still fire at the boarded ship - Turrets don't seem to care about Boarding Op Behavior or that the ship is boarded.
In addition, I believe greater awareness of Boarding should be applied to friendly/allied/owned AI, such as:
- Preventing owned ships to fire at non-turret surface elements if the ship is being boarded - ESPECIALLY at Stage II/Stage III.
- Preventing friendly/allied faction vessels from destroying a boarded ship with your marines in it if it's turrets have been destroyed.
i.e. prevent AI destroying boarded ships if the ship is disarmed and boarded.
As it stands, it can be rather frustrating having to hastly cancel orders and try to move owned ships away from the boarded target - and owned ships might still proceed to destroy the boarded ship. A big boarding operation failing because an AI-owned ship decided to throw 5 torpedoes on a disarmed vessel is bad.

As a bonus report: it seems when reaching Stage II/Stage III of boarding, the Attacking Marines (your marines) counter sometimes reset to 0. This can also happen if you order a subordinate or a ship that was participating in the boarding operation away (cancel its boarding orders, after it launched its marines). So Attacking Marines most of the time show 0 with Very High Risk, and keeps the Boarding window not working as intended.
Side note: the boarding feature in this iteration is the best in all games, so so much smoother overall. I believe those (along with other reported issue about pods sometimes not being launched by AI ships) are the biggest issues I found with it, and if/when they are fixed it will be great. Well done.
Thank you!