(Is it only me? I find these "questions" a bit odd......)
Ok, taking them on face value, Regarding what it takes on the "Society's" end to send in troubleshooters:
The *key* thing is what the local congregation(s) members are thinking about a particular issue.....got to keep the folks "happy". If the "Society" (your words) think the rank and file's assumed "happiness" is being negatively impacted by some local issue, they will look into it, no matter what it is, big or little. Gotta keep the troops "happy" and "contented". Congregation members have no idea how much crap they can stir up with a whining letter, even if the local BOE has already dealt with it and the letter writer knows that. Remember the "Society" doesn't give a "rat's ass" about individuals or about individual's time answering bogus stuff.
In most cases, they first would write the local BOE, possibly CC'ng the CO, asking for an explanation of what they were hearing back east: example: "....We attach a letter from (name of complaining person), wherein she/he claims that an elder in your area is (fill in the sin or accusation here). Is this true? Has he been counseled about this? Please explain how he can be 'free from accusation?' We look forward to your early answer to our questions".
This is not the only way I've seen things like this approached, I've also seen a CO/DO duo get into "investigatory" mode.
On a related thought, my experiences are a bit dated now, but one needs to remember that the CO has a lot of "power" and a big say in what goes down. He has great flexibility, for example: One CO blew through the Circuit and just flat "stirred things up", first time around.....many elders and MS's got deleted, generating a lot of "buzz" about him being a hard case, etc. At the Circuit level, he re-arranged the Circuit assignments of most of us, arbitrarily, like musical chairs. Upon the occasion of him rotating out as CO, he confided in me that he "always stirred things up" upon serving a new circuit, as it made things easier for him...made the BOE's more likely to "jump" when he barked.
This thread has brought back to mind many (wasted) hours spent writing letters regarding complaints made about individual elder(s).
--Dannyboy