But they're speaking, not singing, right? Not that Swedes can't sing in good English, of course (Gedda has been mentioned as an example). And there are plenty of native English speakers whose diction in their own language is inferior to that of some foreigners. English, of whatever variety, does present some interesting challenges, as wkasimer points out. For that matter some Americans speak what purports to be my language so sloppily that I'd like to have them arrested for linguicide, or phonicide, or something.
This raises the interesting question of what sort of English to sing in - or, more acccurately, whether to sing in any particular spoken form of English at all. Neither British nor American singers make exactly the same phonetic sounds in singing - classical singing - as they do in speaking, Not only are regional accents eschewed, but there's a bit of internationalization most likely resulting from the Italian-based tradition of clear, open, non-diphthong- inflected vowels. It can be easy to spot native English-speaking singers when dipthongs creep into their pronunciation of other languages, commonly on the short "e" and long "o," and it's similarly easy to spot a foreigner speaking English when he fails to get the diphthongs right. But English-speaking singers singing in English need to make adjustments too: Americans generally need to modify their typically strongly rhotic final "r," and Brits need to open up their often very closed "a" as heard in words such as "wall" and "war." It's sometimes possible to tell whether a singer singing in English is British or American, but not always. Unless you're Enry Iggins, of course.
A singer might choose to retain and emphasize her regional accent for a specific artistic purpose. Sometimes we want to sound distinctly British or American. Moreover, it can be great fun aping the speech sounds from the other side of the pond. I once served as accent coach for a high school production of "Oliver," and even if I wouldn't have fooled a real Cockney we did at least have a blast playing make-believe. Some of the kids were actually pretty good at sounding like 19th-century London street urchins. "Please, sir, I want some more" has not a single vowel that's pronounced as anyone this side of the Atlantic does it (except possibly the schwa in "some"), so if you can say that properly you're well on your way to Eliza Doolittlehood.