The government wasn't so sure either. You had to sign a form saying you wouldn't export the CD player to hostile foreign countries, I guess that might use the CD player lasers to enrich uranium.
I think it was actually the computer chip that was (and is) in every CD player. Back in the 80's, there were export controls on computers that could execute more than a certain number of MIPS.
The computer chip in a CD player is a custom chip for a specific purpose, but it probably exceeded the threshold -- because the export controls didn't make a distinction about WHAT the chip actually did.