Even if he did lie, that's absolutely protected speech and the FCC is out of line. Every Constitution-respecting American knows this and would be against the FCC saying anything no matter what party was in charge.
In fairness to the provision, I think it's outdated, and I've argued against its relevance and that it seems unlikely to me to stand up in any court that interprets 1A jurisprudence to a modern standard, but the law exists and exists specifically to prevent against broadcast lies.