Using the models we've built so far, it's easy to see how this is censorship. Analyzing the concrete parts that go into building the web page in the first Third Voice screenshot, there is the glaring intrusion of the comment from "shaina" that the author of the web page clearly did not intend. That is certainly content not coming from the author or even the reader, but from this "shaina" person. Without consent from both the web page reader and the web page author, such an addition clearly meets our definition of censorship.
This is not just academic. One of the most popular uses of Third Voice, measured by "pages with the most annotations" (Third Voice provided a little graph showing the "most active" pages on the web for some period of time, and while I obviously can't point to it, it allows me to know this was one of the most popular uses of the program; "Say No to Third Voice" monopolized the top position for a long time), was to visit the sites protesting Third Voice and attempt to "shout down" the protest sites through sheer volume of posted notes, sometimes so many that the browser would crash for some people. I'm almost sorry the program is shut down now, because you simply have to take my word for this: Even if you believe for a moment that Third Voice users would indeed use the service for the noble causes the creators claimed for it, a quick cruise around the system indicates that it was only rarely used for that, and you would quickly become disabused of the notion that it was being used for "debate". What little content on the service that was truly related to the page was almost entirely of the "shout-down censorship" type. Just as the readers have the Free Speech-based right to visit a web page, read it, and draw their own conclusions about the content, web page authors have the right to present their material without "interruption" from people, even if the reader desires that interruption.
Going even further, there is nothing special about "annotation". The symmetry of communication inevitably bites those who wish to make exceptions. If we try to make web annotation legal by dropping the requirement that the content author consent to the modification, then that applies equally to the annotations themselves. Many Third Voice users would have cried "Censorship!" if Third Voice started taking down notes for any reason other then community standards (and many certainly cried "Censorship!" when my techniques were used to prevent Third Voice from working on certain web pages), or even modifying them to suit their own purposes, but once you forfeit protection for the author, your own communication loses that protection as well. If anybody who has the technical ability can modify a web page by inserting content, then there's no way to limit that to just "annotation" or "good" uses; that means if somebody at AOL intercepts an email you send via their service and adds something to it "just because they can", there is no basis for complaint.
Perhaps the best way to look at this is to look at the Chain of Responsibility for the communication. For the original web page, only the original author of the web page is on it, since all other entities who are involved with transmitting the message do not affect it. When viewing a Third Voice "enhanced" web page, there's the web page author, the Third Voice company (who controls content via their centralized server), all the other people who used Third Voice to leave a note, and the user of the web page itself, because they installed and turned on the software.
One of the consequences of our right to free speech can be expressed as the right to control the chain of responsibility to the extent possible. Without the ability to deny others the ability to modify our messages we can not have confidence that what we are communicating is being expressed. The only possible ethical justification for Third Voice I saw given by its defenders is that a receiver has an ethical "right" to modify the page as they see fit. The reason this seems so plausible is that it is partially true; once the message has been received the recipient is free to do with it as they please in their own possession. But it is not completely true, because the recipient does not have the right to add other people to the chain of responsibility, allowing them to modify the message. Once the intended message of the author is altered or destroyed, the value of the web page to the author is also destroyed, and the end user does not have the ethical right to do that.
This is another way of looking at how the breaking of symmetry inevitably bites the very people who wish to benefit from it. Note that the end user does not have the power to insert the other entities onto the chain of responsibility. When two parties are involved, changes in the relationship require the consent of both parties; it's the same fundamental reason that when someone invites you over for dinner, it is impolite to invite somebody to come with you against the wishes of the dinner host, or when two people sign a contract, it takes the consent of both to change it. The wishes of the end user are not sufficient, so if we wish to claim that behavior is ethical, we must find some other basis to say that such external addition is ethical. But in the final analysis, the only basis that is even a candidate for that is mere technical ability to add other entities to the chain. Therefore, by opening the door to annotation we open the door to arbitrary content manipulation by anybody who has the technical ability. Annotation is merely a convenient term we give to certain types of content modification, but there is nothing fundamental about it; there are no sharp lines you can draw between it and more conventional content-based censorship of all kinds. In all cases, the ability of a sender to express themselves without interference from outside parties is irretrievably compromised.
In the long run, communication's value is directly connected to the reliability of the transmission of the information it contains. To allow messages to be arbitrarily degraded for a small short-term gain will inevitably make the system useless for all in the long term.