This is a known issue with bow-using companions. (Possible bug?)
Aela the Huntress does it too. You could get her a legendary quality daedric bow and she'll still pull a hunting bow out of thin air to use.
There is a known bug, that Aela won't equip any other than her default bow. It may occur from removing her default Hunting Bow from her inventory in an attempt to make her use a new bow, in which case it appears the character resorts to using unmarked-inventory default Hunting Bow
http://elderscrolls.wikia.com/wiki/Aela_the_Huntress
I've noticed that it applies to any follower who comes with a default bow. If you're on PC, there is a fix listed there using the console you can try.