They are both (Liam/David) playing a game that involves moving media pieces around, and Cameron has just called Fox's bluff - for Liam to win now something has to go demonstrably pear shaped in the next year, in which case he becomes a sort of messianic figure, while a successful culling of defence that doesn't backfire badly inside a year means Cameron wins instead.
Liam's letter was a political move, and I doubt very much he really cares or even understands what he allegedly wrote, other than as a vehicle to obtain some advantage on the greasy pole - matched to an uncanny degree by David's ability to understand what dropped through the mailbox.
They're both politicians, they wouldn't recognise morality or common sense if you wrapped it in a brick and smacked them over the head with it.