CNN is not broadcast over the air - it is cable, so the FCC does not have jurisdiction.
Not exactly. The FCC does have some limited oversight over cable programming. From the
FCC Cable Television Fact Sheet:
Indecency and obscenity. Generally, the rules concerning the content of programming on cable channels are not as strict as the rules concerning programming content on non-cable channels. If you object to programming on a cable system, you may contact the FCC to determine what rules may be applicable and what action may be appropriate.
I haven't found anything about whether the subliminal perception rules apply to cable. There is a
regulation promulgated under the broadcast station rules - 47 CFR 73.4250, which refers to a public notice promulgated in the 70s, before the advent of cable TV.