The DC didn't need modded, which was a bizarre decision.
That's because the games were on a proprietary format - GD-ROM not CD-ROM. You can't copy/read a GD-ROM from a PC cd drive.
The playstation always had the copyprotection system, but later decided to write additional logic into there games to detect if a system was operating with a mod chip or not.
I don't think the adoption of the copyprotection scheme was in response to CD-Rs at the time, but to the pirate/bootleg companys passing games off as the real thing, as CD-R drives were extremely expensive in '94/95 - about $1500-2000 and the CD-R media was pretty horrible at the time. Bootleggers were the main focus.