This example on Page 118 of Dogs in the Vineyard intrigued me:
"— They want the Dogs to buy stuff, so they’ll try
to break their stuff too. They don’t want the Dogs to
pronounce that it’s okay for the town to rob the store —
because if the Dogs say it, it’s probably not false doctrine.
That’s what Dogs do, after all." (emphasis mine)

The question -- Can the Dogs change doctrine, both pragmatically and theologically?

Here's an example so I can ask what I mean more directly:

Pride: Brother Lemuel has romantic interest in his neighbor, Brother Nephi, and the feelings are mutual. Brother Lemuel believes that their sex is transcending God's law.
Injustice: This sinful love is putting the town's Steward, Brother Lehi, in an awfully difficult position. He has to choose whether to uphold the King of Life's laws and the law of the Territorial Authority. Nephi's mother Sariah knows about their love and has to make the same choice between righteousness and comfort with sin.

Sin: Brother Lemuel and Brother Nephi have sex in the church for extra blasphemy points. Sister Sariah lies to cover up the sins of her sons. Brother Lehi commits the sin of worldliness by displaying comfort with the sin, refusing to force them to stop or intervene, remembering his own past with the Dogs and his interactions with his partner. He thinks it's just a stage the two will grow out of.
Demonic attacks: The demons are causing tools to break on Brother Lemuel's farm more often, driving him to visit Brother Nephi more often for replacements (Nephi's really handy with repairing broken shit!). An out-of-town trader who just happens to carry giant supplies of whiskey is passing through, and Sariah's water well mysteriously dried up, resulting in her having to go to town for water and be tempted by the sweet release of alcohol. Brother Lehi's church has started falling apart, requiring two strapping young men to fix up the place (Nephi and Lemuel) pretty much weekly, if not more often with all the mysterious damage. Meanwhile, dark clouds are gathering outside town -- the storm is big enough that, if it comes through, all the crops will be wiped out.

False Doctrine: False Tenet 1: Gay sex is inherently supported by the King of Life and is a way of glorifying His name. Believed by Brother Nephi and less so by Brother Lehi.
False Tenet 2: There is no God. Believed by Brother Lemuel and Sister Sariah.
Corrupt Worship: Nephi talks Lehi into helping him with a ritual involving slicing up a pig, Old Testament style, in worship of the King of Life, to consecrate his holy bond with Brother Lemuel.

False Priesthood: Brother Lehi, our poor Steward, unwittingly becomes the head of a cult by deciding to preach that love of all kinds is perfectly acceptable with the proper respect for the King of Life. He introduces the pig-slaying ritual to his congregation. Lemuel and Sariah are totally into that and some of the other members of the congregation are starting to let their eyes wander. Soon we're gonna have all kinds of sex problems if this doesn't stop.
Sorcery: Since the demons are totally down with a sinful orgy of sexual sin, they decide to make the Church especially windy, cool, and refreshing on days when Brother Lehi is giving his false worship speeches. They're also amplifying any sexual desires in the population. They're still doing all their other shit though and going to use that massive storm to wipe out the crops.

Hate and Murder: Brother Laman is sick of this shit and beats up Nephi for his choice of sexual company. In return, Lehi subtly encourages Lemuel to murder that asshole. Accordingly, Brother Lemuel burns down Brother Laman's house with Laman inside.

Laman's cousin Sam wants the Dogs to end this shit immediately and have all the sinners murdered.
Sariah wants the Dogs to go away and leave her child and priest alone. She'd also appreciate if they got rid of the whiskey merchant.
Ishmael, the whiskey merchant, wants the Dogs to try some of his delicious liquor and not interfere with his peddling.
Nephi wants the Dogs to participate in a Greek-style sexual orgy in praise of the King of Life.
Lemuel knows how the Dogs work and wants them dead.
Lehi wants the Dogs to toss out the whiskey merchant and also to definitely not find out that he supported murder of one of his Faithful.

The Demons want the Dogs to get the fuck out of town. They want Zion to turn into an orgy of sex and murder. If the Dogs are going to stop that, they're going to speed up their storm and hope the storm wipes out the town's crops before the Dogs can stop all the sin, making it a race against the clock.

If the Dogs never came, the town would definitely become an orgy of sex and murder, with the Faithful murdering other Faithful with different believes, and all the townsfolk cheating on each other because of a lack of official intervention from the Steward. The storm would pass over in order to allow this place to continue existing and become even more of a nuisance and eventually a blight upon all of Zion.


With all that done...
Brother Harwell, Dog's Watchdog, arrives in town with his spunky junior sidekick Sister Lewiston. And here the question arises:

Pragmatically, can Lewiston and Harwell toss out the demons, beat up Lemuel for murder, declare gay sex to be totally okay in God's eyes, and move on? Would the townsfolk buy it, since a Dog said it? Can the Dogs simply say 'yup this is not a sin' and in town law, at least, gayness is no longer a sin?
Theologically, can Lewiston and Harwell do this? Will the demons actually stop recognizing gay sex as a sin and melt at the power of the Dogs to change doctrine? Will the Stewards at the Dog's Temple be pissed at their representatives for twisting the doctrine that severely? Will the King of Life simply shrug and say 'yeah that's alright now'?

I hope this explains my question well! This question comes from a queer Ex-Mormon, so I apologize in advance if that scenario sounds homophobic or otherwise prejudiced -- definitely not intended that way!