Also to the OP, most people I know who insist on doing Asian caricatures combine the L and R thing indiscriminately, as in “Helro, I honorable Bluce Ree.”
Sir Rhosis
I don’t know about Chinese, but in Thailand (another Asian country with a similar tonal language and sound set), the Ls and Rs are pretty often reversed in spoken English. (They have their own idosyncacy that ending Ls are pronounced as Ns, which is consistent with their own language structure. Ironically non-native Thai speakers also tend to have trouble with Ls and Rs as used in Thai. The Thai word for foreigner is farang*, for example, but often pronounced as falang (and often transliterated. The reason for the confusion is that the L sound and the R sound in Thai and English are not perfect equivalents but more like very close approximations. In Thai they seem to also change within the context of the word (by position in the word and depending on placement of nearby vowels). My suspicion is that at least in some Chinese languages some of this occurs. Point being there may well be a strong basis for the “stereotype”. Chinese in Hammond, Indiana (where the film is set) would have most likely been recent immigrants at the time.
*More or less, the language is not quite that easily transliterated.
I read a book called The Language Instinct in which the author said this was because oriental languages never string constanant sounds together. Each are always immediately followed by a vowel sound. An example he gives is how its impossible for them to say ‘strawberry’. It comes out ‘so-to-ro-berry’.
BTW, Hammond, Indiana was, according to their website, a city of 70,000 in 1940. So not exactly “small town” America, by standards of the day at least, but not a booming metropolis, either. It is located just south of Chicago, so one would assume that if there were a few Chinese restaurants in Chicago then, it would not be unlikely to have one enterprising Chinese restaurant in a nearby community.