With a quick look through the Baha'i library, and a few other resources I've got, the earliest reference I could find to this notion that criticism must be confined to appropriate channels (i.e. Feast, Convention, and letters to the institutions) was 1988. The first official mention is in the UHJ's *Individual Rights and Freedoms* letter; the first unofficial one was in a talk by Firuz Kazemzadeh in March of that same year. This is an innovation; a response to the fact that Baha'is were finally starting to express themselves in more public forums. Since then, it has been exalted to "fundamental Baha'i principle."
Now, my first individual exposure to the idea came when I was a brand-new believer in 1985. I was told about certain people in the LA area that were criticizing the administration (Oh, gee, ain't it awful!), and that criticism is absolutely forbidden in the Baha'i Faith. However, I was too new to realize that this notion was sheer Kitab-i-Hearsay -- and indeed, it may have been "planted" Kitab-i-Hearsay, originating with Baha'i administrators and being passed on informally, as it was to me. In any case, the idea that criticism is invariably destructive of unity is something that may be embedded in Baha'i culture, but it has nothing whatsoever to do with the Teachings.
As far as the "channels" go -- they're a joke. Take a criticism through channels, and you are even more likely to bring trouble down on yourself. In fact, the people that got into trouble with the administration did so partially because they actually had more interactions with it that your average Baha'i would. (In fact, it's the reason that other Baha'i dissidents have a stronger focus on the administration that I have had in my writing; it comes out of a difference in experience.) Indeed, letters to the UHJ have actually been held against people and resulted in their being forced out of the Faith. It's the fastest way to get a file started on you.
Even if that doesn't happen, it ends up being a "divide and conquer" sort of strategy, where critics are isolated, and basically told why the status quo must remain. It sounds oh-so-reasonable: Why didn't you just write to the institutions about it? Because nothing happens when you do -- " consultation" in this instance just means the opportunity for them to "talk you 'round".
Baha'i really are in a bind that way: Problem-solving through consultation is a part of our identity. We're a very talkative religion. :-) We piss and moan about the long and boring meetings; they are even a rich source of Baha'i humor. But let anybody try to take those meetings away from us -- as the NSA did with Unit Convention -- and you hear howls of protest. What were *dialogue* and Talisman anyway, other than forums for Baha'i consultation? But speaking openly and frankly, as 'Abdu'l-Baha' and Shoghi Effendi has given us the right to do, puts a believer at risk. Once your opinions are out there, you can be called on the carpet for them. It is assumed that a deepened and sincere believer will know ahead of time what you are not supposed to say. Say the wrong thing, and you are assumed to be undeepened and/or insincere.