Here's the problem with the region of Balquhidder: unlike Mamore (of the Camerons) or Appin (of the Stewarts), this is an area that doesn't belong to any single clan in particular. There are lots of different smaller groups struggling amongst one another.
Luckily, the door Alan knocks on first belongs to a member of the Maclaren family, who are allied with the Stewarts. It's a man named Duncan Dhu.
Poor Davie is immediately put to bed while they call a doctor. He's laid up for a month before he can go out on the road again.
Davie is surprised by Alan's loyalty in staying with him until he's healed enough to travel.
Here's something interesting: everyone in the neighborhood knows that the government is looking for Davie. After all, there aren't that many young Lowland guys traveling with Alan Breck Stewart. But no one turns him in.
Not much happens during Davie's stay in Balquhidder, except that he meets Robin Oig, a son of Rob Roy.
Rob Roy was a member of the Clan MacGregor. He led his people in an uprising against the English in 1715. Like Alan Breck Stewart, Roy was also an ardent Jacobite. Check out this account for more on Rob Roy – although, fair warning, the account's a bit biased against the Campbell family.
Robin Oig comes to the Maclaren household to tell Davie that he has heard that Davie's name is Balfour. In the Battle of Prestonpans in 1745, Robin Oig's brother broke his leg, and the surgeon who fixed it was also named Balfour. As a result, says Robin, if Davie is a close relative of that Balfour, Robin is there to put himself at Davie's service.
Davie is embarrassed to admit that he has no idea if he's any relative of that Doctor Balfour.
Robin washes his hands of Davie and walks out the door.
On his way out, Robin bumps into Alan.
They size each other up and exchange a few insults about Campbells and swordsmanship. It looks like it's going to come to a fight, so Duncan Dhu, the owner of the house, jumps in.
Duncan suggests that they have a pipe-playing contest.
They play back and forth for a bit, each talking smack about the other's performance, until Robin Oig finally manages to win the day by playing a tune beloved by the Appin Stewarts. Alan hears the song and is so moved that he tells Robin, "I am not fit to blow [the pipes] in the same kingdom with ye" (25.49).
Thus, the quarrel between Alan and Robin Oig is resolved.