Like Forensic, I can’t think of any steel-core 32s (7.65 Brownings). Many people think of steel cores when they put a magnet to a projectile and find it is magnetic. In .32 auto, this is normally a result of a steel jacket, not a steel core. The only way I know of off hand to confirm core material in a projectile with GMCS or CNCS FMJ bullet jacket is to pull the bullet and put the very corner of a small magnet to the the exposed core.
If the bullet is drawing a magnet but it is suspected that the jacket is NOT steel, you can put the corner of a very weak magnet at the very tip of the bullet and it usually (note that I said “usually”) will not draw on a non-magnetic jacket. If you use a strong magnet and the core is steel, it will jump right to the magnet when held to the tip (or anywhere else on the bullet).
This is one reason why it is helpful to have a selection of magnets of different power, about in your cartridge room.
I suspect that the .32 used in the test described was a steel-jacketed bullet with a lead core, mistaken to be a steel-cored bullet.
If anyone knows for sure about any steel-core .32, let me know. If I have a dupe, I will rip one apart. In the absence of a dupe, I will test one every way I know how to try and confirm if the core is steel. I have a fairly large selection of .32 auto rounds in my collection.