I made the exact same build three times and got the same results.
I switched up the stats the fourth times and got a slightly different recipe set.
Then I made a toolcrafter and had basket recipes.
Interesting. Try str 60 sta 60 agi 50 dex 60 int 70 per 70 charm 60 and spirit 60 and see what happens. Those are my stats, with shovel and axe and unarmed combat, and I got the storage basket both times I rolled it.