As far as, "Kindly Man can never end up as the Agenda of someone who is not its owner." Was that a statement of what you believe, or is that stated in the rules?
It's my interpretation of the rules. And it is correct.
Start with this:
"(4.11) Agenda Cards
Agenda cards are not considered to be in play. Further, the effects of an Agenda card cannot be canceled."
So, right there. Agenda cards are not "in play." That means that when a character becomes an agenda, it must leave play in order to become that agenda.
Then, as you quote:
"(3.31) Changing Control and Leaving Play
When a card leaves play for any reason, it always returns to its owner's discard pile, dead pile, hand, deck, or shadows area (depending on the specific circumstances)."
This stands for the fact that when a card leaves play "for any reason," it goes to its owner's corresponding out-of-play area. When a character becomes an agenda, it leaves play (as established above).
Now, you seem to be arguing that this list of out-of-play areas must be inclusive, and because "agenda" is not listed, the reversion of the card to its owner's corresponding out-of-play area does not include "agenda," even if it is an out-of-play area. To me, that is a pretty bad argument. Not only was this FAQ entry written years before the "character becomes agenda" effect existes, but the the bit about "depending on the circumstances" can cover any out-of-play area.
We went through this with Shadows too, by the way. People tried to argue that a card going from play to the Shadows area was not leabing play "for any reason" and that since "shadows area" was not included in the list of out-of-play areas, control did not revert when a "stolen" card was returned to Shadows. The ruling came down that "leaving play" was the operative term here and that the list of out-of-play areas was not to be considered inclusive within the reversion of control rule long before "shadows area" was added to the list.
So, short version: Agendas are not in play. Therefore, when Kindly Man is killed, it must physically leave play in order to become the agenda. Cards that leave play "for any reason" always return to their owner's appropriate out-of-play area (the list in the FAQ should not be considered "all inclusive," especially when FFG invents a new out-of-play area that can be reached from play).
And as a result, there is no situation in which Kindly Man will end up as an Agenda on any House card other than the one belonging to its owner. And since Kindly Man is "House Stark only," the practical upshot is that Kindly Man will never end up as an Agenda on any House card other than Stark.
In order for a card to return to the owner's control it has to leave play which happens in step 6: End of Action. Moribund Cards Leave Play.
But before that happens, Kindly Man's passive ability would trigger in step 4. Passive Abilities (now triggered) are initiated.
Thus, in step 4 the card would check, the contollers house card for Agenda's.. if none it would resolve and attach, and if an agenda is present it would resolve and fail.
You are not resolving the replacement effect properly, nor are you treating the "agenda" state as the out-of-play state that it is.
Kindly Man's effect is a replacement effect, just like Doubting Sept, KotSea-Damphair, anything Stalwart, etc. That means that when a kill effect would send the card into the "moribund:dead pile" state, it instead sends it into the "moribund:agenda" state, assuming the replacement's effect's restrictions are met because its controller doesn't have an agenda. (This happens in Step 3, during the resolution of te kill effect, not in Step 4 - after the effect has already resolved and the card is already moribund.) Then in Step 6, the moribund card leaves play and goes to it's owner's out-of-play area corresponding to its moribund state.
In the end, what I have described in the above post (and in other threads) is correct - if you take the entire FAQ into account and do not insist on supplanting the meaning of "leaves play for any reason" with the non-inclusive list of out-of-play areas. But, don't take my word for it. Feel free to send it into FFG.