What I have in mind here is the kind of social anonymity discussed in the article, not the more rigorous kind of anonymity offered by Tor.
On the technical side, I supposed you'd have a central recipient of $anycoin on the BBS server that would authorize a user to post when it received a given amount of $anycoin from that user. Other posters could possibly exploit this by trying to correlate the time on someone's posts with the transactions on the blockchain to find out what "wallet"/address is behind the posts. Perhaps this could be mitigated by the server introducing noise to the displayed time. I'm not sure how important this is to anonymity of the non-technical kind (one where you could subpoena the access logs from the website the discussion takes place on and where people routinely click on links).
On the technical side, I supposed you'd have a central recipient of $anycoin on the BBS server that would authorize a user to post when it received a given amount of $anycoin from that user. Other posters could possibly exploit this by trying to correlate the time on someone's posts with the transactions on the blockchain to find out what "wallet"/address is behind the posts. Perhaps this could be mitigated by the server introducing noise to the displayed time. I'm not sure how important this is to anonymity of the non-technical kind (one where you could subpoena the access logs from the website the discussion takes place on and where people routinely click on links).