If the "political speech" is demonstrably false, why don't politicians simply bring a lawsuit against the perpetrator? It would only take a few victories in court before all political campaigns straightened out/up.
It isn't that easy. Most of the liberal politicians who lie through their teeth in campaigns would be quick to accuse their opponents of lying. This is because by the time their opponents would be able to prove they weren't lying, the campaign would be over with a landslide victory for the liberal. This isn't about truthfulness in advertising, it's about shutting up political opponents.