Also, some people either can’t or just don’t know how to pronounce something in another language. My mother sometimes tries to maintain the ‘correct’ pronunciation of foreign words, such as Italian words (she studies Italian). However, she finds it impossible to trill her [r]s. So, when she says one isolated Italian word that has an [r] in it, she 1) tries to trill but fails and messes up the rhythm of her speech, or 2) pronounces the vowels correctly, but rhoticizes the [r].

I would say that this isn’t limited only to native English speakers. In Italy (my current location), people pronounce English words according to Italian pronunciation and stress. Cantonese speakers (my fiance is from HK, as are many of our friends) tend to map Cantonese tones and rules of pronunciation onto isolated English words quite a lot.

I think there should be a distinction drawn–one which you don’t make in your post–between the pronunciation of foreign words in isolation (i.e. 1 foreign word in a string of native language speech) and in linguistic context (i.e. a non-native speaker of a language).