That's a dangerous game. There is nothing a fake could say, no matter how ridiculous, that wouldn't convince somebody that the real person said it. Maybe they believe the politician already kicks puppies, maybe they hear what they think is a "reasonable" (yet still wrong) interpretation instead, or maybe they're just stupid. Doesn't matter, because now they're going to play telephone with their friends and family about the stupid thing the politician didn't actually say.
Even if it works, what's the upside? Now your brand is associated with negativity and people are thinking "maybe they didn't say that, but why take the risk? X is a safer bet".
Probably something for domestic intelligence agencies to do with their local politicians. It does seem like a reasonable defense. Release the ridiculous deepfake covertly so it's assumed to have been done by some rando for the lulz and then release a statement a few days later talking about the dangers in a world occupied by deepfakes.
It's kinda got me curious: what recording would be so obviously fake?
Even if it works, what's the upside? Now your brand is associated with negativity and people are thinking "maybe they didn't say that, but why take the risk? X is a safer bet".