That's because they are putting on an accent! American choirs are in general trained to make some adjustments toward BBC English, notably a slight roll to inner 'R's and softening of some dipthongs and the trailing 'R'. Accents do shift somewhat in singing, but even without that, American choirs would tend to sound a lot more like Tammy Wynette than Paul McCartney if they didn't compensate for it.
Accents are definitely more malleable singing than speaking as Samer has described well.
I think anybody with a good ear singing that kind of music naturally ends up sounding close to BBC without putting on the full accent, just because it sounds better - that's what I was describing. You're right that choirs are taught to do some of that and the result is better.
Tammy Wynette? Yes, that's what the raw American voice sounds like to many Brits and Europeans. (American dog
sounds like darg
to British ears.)
Paul McCartney? I don't think a choir singing even in a modified Scouse accent like he has (or at least puts on - some say Sir Paul really has a London accent now) would sound too pretty: 'I lift oop my eyes ernto the hills: from whence coometh me help.'
We have had singers here at SVS that roll their r's when they sing. I think it has to be one of the most annoying things I have ever heard.
AFAIK the main distinction in Byzantine Rite singing, at least in the Russian recension, is between choral singing and kliros singing. The latter, often recto tono
(monotone) or nearly so, is supposed to be in a soft, flat vibratoless voice so exaggerated rolled r's in that would
be out of place. (Not to be confused with the clicked initial or inner r you sometimes hear older English people or non-native speakers use, which sounds fine.)
In choral singing in English no problem - I think that would use the same kind of voice as Anglican choral stuff. True of the Western-style choral works by Russian composers, the staple of Russian Orthodox churches.