Did Apple introduce a white list of hard drives (for MacBook Pro A1278)?
No, there is no white list of acceptable replacements for storage disks held in firmware.
Apple doesn't make their own drives. Hard drives are made for Apple by Toshiba and Seagate, and the supplied drives are not 'custom built': they just meet a certain spec.
I've replaced the hard drive on hundreds of Macs and never had a problem of this sort.
You say that the SATA cable &quot;looked in perfect condition&quot; and you &quot;tried to make sure that the problem was not the cable&quot;. You can't tell by looking at it if the cable is faulty. What did you do to test the cable?
I would definitely try replacing the SATA cable, as they are a well-known point of failure on those models. The fact that the drive works externally but not internally would suggest that.
(Though to be honest, I would recommend getting a 1TB SSD, as this would significantly improve your Mac's speed.)