Normally, people use magnets in an attempt to tell if the bullet CORE is steel, indicating armor-piercing (AP) ammo.  But bullets with steel JACKETS, such as the ammo you describe, will also stick to a magnet.  Perhaps the person doing the testing doesn't know the difference, and needs to be educated.  Or, maybe they won't care, and won't let you shoot your ammo regardless.

The problem is that a LOT of surplus .308 uses steel jackets.  You may want to check out British or Israeli (IMI) surplus.

-Troy