Aladdin, Ali Baba and Sinbad the Sailor were well-known long before Disney.

There's even a major Chinese company named after one!

Very likely yes. I was very familiar with this story, and other "Arabian" tales, well before Disney made the original animated version.

We also had Grimm's fairy tales, which I loved reading, and nowadays am reading to my daughter, to her delight. Yes, with beheadings and child-eating monsters and witches.