This is something I don't remember noticing before: Siddgeir's disposition towards the player immediately increases from 0 to 1 when the courier approaches them to deliver "Letter from Jarl Siddgeir of Falkreath".
While this may be by design, and therefore not a bug, it seems bizarre for several reasons.
(1) You haven't actually met the Jarl yet, and when initiating dialogue for the first time he says "Good to see you. Finally someone useful is around." This dialogue line indicates that you are already his friend (i.e. his disposition towards you is 1).
(2) After introducing yourself, there is an option to ask him how you can help. He goes on to tell you how he would like you to kill some bandits that he previously had some "discreet" dealings with.
(3) When returning from killing the bandit, he says he likes you, and offers the option of buying land from his steward. At this point, his disposition towards you increases from 1 to 2.
It logically, at least to me, seems like Siddgeir's disposition towards the player should start at 0, then increase to 1 once you've killed the bandits. Maybe there is an explanation for this, such as him stating in his letter that he has heard of your fame. Though, in my case, I hadn't even read the letter. I realize that Bethesda's design decisions don't always make complete sense, and that this doesn't necessarily mean it is a bug in the game.
Issue Data
Issue #33870: Siddgeir's disposition towards player when letter is received