You have it backwards. Conflating free speech with paid ads isn't about whether the paid ads are free speech, it's whether paid ads are necessary for free speech. That's an important distinction, and is clearly the argument the OP is making.
Zuck never said it explicitly, but it's strongly implied from his conflation of free speech and paid ads that he thinks paid ads are necessary for the freedom of speech.
That's where the fallacy lies. Paid ads, while being free speech, skew the messages' reach. It's cute that he tries to use a grassroots message as the upside, but it overlooks two massive problems that are pervasive on his platform.
1. The deeper your pockets, the louder your megaphone. It doesn't really matter that the little guys can also buy political ads if the big players can drown them out. In fact, I would say it has the opposite effect than the one he suggests. A grassroots effort with a compelling message can make waves without political advertising, e.g. the Arab Spring. But in an environment where most political messaging is ad-based, a small effort will never have enough resources to compete with a larger foe.
2. There is no accountability in the political ads. In one example, there are at least 10 "different" pages all disseminating the same false messages, coordinated at the same time. Yet Facebook says these are unrelated pages. Being as there is no reporting of who is funding the ads, it's impossible to tell if it is a candidate, a PAC, or a foreign power backing them. And as we've seen, that lack of accountability can be very problematic.
We have a lot of rules about political speech because we have seen over time how it can be abused. Social media did not exist at the time, but now it has more power than any other form of media. Twitter sidestepped the whole issue, and kudos to them for it. Candidates and PACs can still get their messages out, but now it has to be on merit rather than money. Facebook is going the opposite direction, and that's a problem.