I believe the other stories you mention are even older.
This is very much an "in principle" thing. In practice, many of these traditional stories have (sadly) become synonymous with the Disney version, so Disney's work is basically the canonical version. This gives Disney a very good sword of Damocles to hang over the heads of anyone else trying to adapt these folk stories: to my understanding if you include a single copyrightable adaptation or embellishment of the original that was written by Disney without "prior art", you're liable to be steamrollered by the lawyer army and be ruined.
This illustrates (IMO, the evils of over-long) current copyright terms rather perfectly: Disney didn't swoop in and benefit at Collodi's or his descendent's expense under the copyright rules of the time. Had current -- heavily Disney-influenced, so presumably supported and wished-for by Disney -- terms been in force then, this would have been a case of Disney swooping in and benefitting at Collodi's or his descendent's expense. Dunno what exactly this means... Besides Disney possibly being quite hypocritical.
And yes, most of Disney's older great hits about princesses and princes (Snow White, Sleeping Beauty, Cinderella...) are based on German folk tales collected by the brothers Grimm and first published in 1812.