@babajayne and @TomasGrizzly My sim has level 10 knitting skill and she had both the bag and basket in her inventory. She lived in Newcrest and I had her travel to a empty lot in Oasis, she couldn't knit at home or on the empty lot.
I downloaded a sim from my gallery that had zero knitting skill but level 10 in several other skills. I took the knitting bag from her inventory and made the downloaded sim pick it up. I told him to knit and he went to a bench sat down and started knitting. My sim that had level 10 knitting skill couldn't knit sitting next to him with the basket in her inventory.
The sim that couldn't knit anything has level 10 in the same skills as my sim that could knit, she was my builder sim with several aspirations done but not the knitting aspiration. I was going to do the knitting aspiration to give her more reward points since I play with whims off and the only way my sims gain reward points is through aspirations. The only difference between the sims was gender, level 10 in knitting skill on the female sim, and level zero knitting skill on the male sim.
I play with aging off in my games and save my builder sims in my library, starting new games with them and getting their skills to level 10, getting build items unlocked so I don't have to use cheats to put locked build stuff on my lots.
What I learned is don't get the knitting skill unless I'm doing the aspiration and make sure to unlock all outfits with the sim. I'll have to upload all knit items to my library so I don't have to rely on the sim being able to knit them when their skill reaches level 10. I think I'll do the same with the fabrecation, candle making, wood bench, etc. so my library will be very full of items that skill leveling sims can make but could be locked out of when their skill reaches level 10.