I'm not a moderator in this site, but starting from my experience as a moderator elsewhere I'd like to say that Emrakul is absolutely right. There are various points I'd like to add (might or might not overlap):

 1. Moderators aren't allowed to discuss these matters other than other moderators *or* the user in question. So even if users had a "correct hunch", we would have either to ignore the question or close it without being able to comment.
 2. Moderators and CM have the tools to confirm if sock-puppetry is taking place (CM even more than diamond mods). Regular users do not have these tools, so conjectures are pointless at best and damaging at worst. And in this case, even if you were right, the proper action to take would be to **flag for moderator attention**, and not take it publicly, because that would achieve nothing except create drama.
 3. A user is theoretically allowed to have more than one account, as long as these accounts do not interact with each other (otherwise we merge them). So if you know that a user has two accounts, that is not against the rules per se. A user may possess a public and a "private" (anonymous) account for any (legitimate) reason, so your public accusation of sock-puppetry will be creating drama again and damaging a user for nothing.

In conclusion, my suggestion (and I think all the mods will agree) is to stick to using flags.