There are actually two types of bad sectors, logical and physical. Physical bad sectors are caused by actual damage to the disk surface which makes the sector unusable. Logical bad sectors are caused by the disk's magnetic surfaces being improperly magnetized -- say by a rogue process or improper shutdown. Logical bad sectors can be regained by properly magnetizing the sectors again. This is essentially what utilities that write zeros to the sectors do during a drive wipe. Of course, these utilies need to be manufacturer specific in order to be most effective. Regardless of type, the drives electronics, not the OS keeps track of the bad sectors. However, the chip responsible for keeping the bad sector inventory only has so much space allocated for this purpose. The hard drive will never be able to keep track of all the bad sectors, logical or physical, that will develop over the life of the drive.
Perhaps your example systems are operating with bad sectors that are not inventoried, and thus the system is able to read the good portions of the sector. A typical NTFS sector is 512 bytes, and many times the entire sector is not used when a file is being written. Then BESR comes along and tries to image the sector. Depending on how bad the uninventoried sector is, BESR may or may not be able to interpret the data correctly. This is just my best logical guess. Regardless, I don't believe BESR was ever intended to be a forensic imaging tool. You are fortunate that the systems are operational enough to extract any needed data. Both of these systems will fail eventually, so extract any needed data sooner than later, by whatever means needed