It does not say that. There is nowhere where it limits the other legal ways under 61.51(f). Also, 61.51(c) does not contain an exception that prohibits use of SIC time for ATP. The 61.159(c) is again one way to apply SIC time, not the only way.

You are not reading the:
"when a second pilot is not required under the type certification of the aircraft or the regulations under which the flight is being conducted" in 61.159(c).

When a second pilot is required under the TCDS or the regulations under which the flight is being conducted, bam, you are back to being able to legitimately log and apply the SIC time.