the Swingle Singers are not jazz, not in the strict sense. Is "jazzy" a better term? So far as my limited musical knowledge takes me, they are singing Bach's score.
Based on this, there is no problem, or even disagreement. MJQ tried to merge the two genres. Sort of like so-called 'fusion' is supposed to be the merger of Jazz and rock.
Non-Jazz groups singing Bach is no problem. Even if they try to 'Jazz' it up. Jazz groups playing Bach is OK, It still remains Bach. Which ain't bad. Third Stream was a dead-end. That is my only point. They never made it work. If they did, share with the rest of us.
Cheers