If they believed that, they would pass legislation to correct the law on which the court relied striking down FTC regulatory authority in this area and allow the FTC to actually do that; not doing that when reversing the FCC rules which mirrored the FTC rules which were struck down demonstrates that that is a pretext, not a genuine motivation.
The FCC rule is being struck down using the Congressional Review Act [1]. CRA provides "an expedited legislative process" [2]. Giving the FTC authority in this area would require passing a real law. (That said, I agree with you regrind the explanation of motive.)
[1] https://en.wikipedia.org/wiki/Congressional_Review_Act
[2] https://web.archive.org/web/20150402230759/http://assets.ope...
Right. But if the real basis of reversing the FCC action is not that the substance is wrong but the regulator is wrong, then you'd expect the fix to the law to allow the FTC to regulate to, at a minimum, be introduced first and highlighted in the debate over reversing the FCC action. (And, in fact, regular laws can be expedited as well, as was demonstrated procedurally with the AHCA, even if the votes were never there to follow through on the expedited process that was set up.)