Under that “theory” any American citizen, who ever sent a letter or e-mail to their state or federal representative, or ever attended a public hearing to give testimony, is no longer a private citizen. That is perhaps the most flimsiest of legal theories I have ever come across.
Yeah, almost as flimsy as saying Donald Trump's joke about "maybe the Russians can find Hillary's missing e-mails" was a legally actionable indication of collusion between President Trump and Vladimir Putin.
Fact is, it's already been used, in a way. Protestors at George Mason University tried went to court to sue conservative students who videoed them, and subsequently posted those videos on line.
The protestors claimed that their right to privacy was violated by the students who posted the videos, but the judge dismissed the case by pointing out the obvious: that the protestors chose to waive their privacy rights when they decided to undertake a protest in a public space.
This situation is obviously quite different, but do you really think that will stop left-wing activists from using that argument in court?