Specifically, the part of the DMCA that the exemption is for is the part that makes it criminal to bypass copy-protection; it does not grant them additional rig

Specifically, the part of the DMCA that the exemption is for is the part that makes it criminal to bypass copy-protection; it does not grant them additional rights to make or distribute copies. There are lots of forms of copying where the copying itself is legal under copyright law. However, the DMCA made it criminal to bypass copy-protection mechanisms, even if they copying itself would otherwise be legal. That's what the exception was for.