Speaking of facts getting in the way, how would slaying the bishop help the we're-gonna-starve aspect any unless there were plans for a bit of cannibalism? 
There's actually quite an interesting and complicated system of honour and revenge at play here!
In the Finnish text bishop Henry and his men are referred to as "ruokaruotsi", which meant the type of taxation where a person of higher standing demanded taxes from the people who lived in the area that he considered his property. If there were no other nobles' lands neighboring his he could freely expand them as he wished.
Lalli was the master of Köyliönsaari and by all accounts a powerful and wealthy man who most likely considered the lands around as his own. For bishop Henry to arrive and demand food and hay was akin of him treading heavily on Lalli's toes in matters of land ownership, no matter whether he paid for what he took or didn't (most likely he didn't pay: there's no note that he would have negotiated the price of food and hay with the mistress of the house, the account that he "left some money in the place where he took food" is most likely a later addition meant to show the bishop in better light). It was the bishop coming over and declaring to another land owner that his house and lands were now under his ownership and had to yield whichever tax he decided to demand.
Since Lalli was not at home when this visit was done he couldn't protect his property and thus suffered a massive blow to both food and hay storage, his reputation and position in general - from a head of the area to someone serving a foreign, invading nobleman. The only thing he could do to regain his position, save face and possibly also to discourage future invaders was to hunt down the group and kill them, which is exactly what he did: he gathered up his men and gave chase on skis and killed the bishop and his men.
- According to the legend, that is. Most likely none of this actually happened and it's just a made-up saint legend constructed to back up the Swedish crown's claim over lands in Finland. It's also possible that the person killed on lake Köyliö was not bishop Henry at all but some other Swedish noble, and that the legend was put together from many stories, naturally spinning the whole tale out of shape and size like Medieval people were wont to do anyway.
