Oh, it was a Disney film all right:

https://www.youtube.com/watch?v=sHKb_XF7CVw

As I often say, this "Sambo" or "Pickaninny" or "Golliwog" stereotype--the image of a caricatured black person with ludicrously thick red lips--is a piece of history, and not just American history either. The stereotype was present across the Anglosphere too, with some British books portraying blacks as that Disney movie did. The different terms all have somewhat different origins, ranging from slavery times for Sambo to the 1870s for Golliwog, but in each of them, characters with the derogatory label shared the pitch-black skin, red lips, and silly expressions.

Such unflattering portrayals of blacks often popped up in all sorts of media, including children's movies/TV shows up till the middle of the 20th century; after World War II racism began to lose ground and Civil Rights movements started to rise for a variety of reasons--the defeat of Nazism discredited ideas of "inferior races," the progression of the Cold War required not just America but Britain and other European countries to treat blacks (and other races) better to win their support from Communism, etc. As a result of this, stereotypes such as sambo/pickaninny/blackface began to be see less as harmless fun and more offensively racist, and eventually fell into disuse--though of course, they haven't disappeared entirely, either from history or even today for that matter; the famous A Wyatt Mann comics rely heavily on such stereotypes.

For more information on the subject, check out Robin Bernstein, Racial Innocence: Performing American Childhood from Slavery to Civil Rights (NYU Press, 2011), and Eric Lott, Love & Theft: Blackface Minstrelsy and the American Working Class (Oxford University Press, 2013). I actually disliked the larger arguments of Bernstein's book, but it contains a decent explanation of what the stereotypes of the 19th/early 20th century were.