I think there's some confusion here: Yes, Paul did pick two random Apple Scruffs off the street to sing backup. However, there are multiple versions of Across The Universe: Four have been released officially, all of which were different, if I am correct: Nothing's Gonna Change Our World (appears on Past Masters Volume II), Let It Be, Anthology 2, and Let It Be... Naked. Let me pick this apart, version by version:
NGCOW: Full speed, bird sounds, wah-wah guitar, no added reverb. Also, this version features background parts, which I believe were recorded on different takes. The first is the Apple Scruffs, who sing "Nothing's gonna change my world" along with John, who are noticeably shrill and unpleasant, hence John's displeasure at Paul's bringing them in. Then, there's the nine-note "aaaaaaaaaah" after each "NGCMW", which appears to me to be Paul and George singing falsetto. The last is the repeated "Jai guru deva"s at the end, which is only one person. I'm not entirely sure who this is. It has a sort of shrillness to it like the Scruffs, but in terms of pitch it sounds like a man's falsetto.
LIB: This version is slowed down, both to change the pitch and to make it the same length as the earlier version that was filled out with bird sounds. It is heavily reverbed and Wall-Of-Sounded, with a string section and a professional choir, presumably brought in by Phil Spector. This is neither the Apple Scruffs nor Paul and George, but is indeed a choir as has been suggested by HeatherBoo. The three sets of backing vocals are not present on this version.
Anthology 2: Take 2 of the song, featuring no backing vocals whatsoever. Much more simply arranged than any of the other versions.
LIB...N: Full speed, no string section, choir, or backing vocals. An echoey reverb is added to the final "Jai guru deva"s, which you'd think would go against the whole point of making a Naked version of the album, but that's what they did.
So, the version in question here is indeed the Past Masters Volume II version of the song, in case that was not clear to anyone.
As for who did what backing vocals, I've explained my view of who sang what. Does anyone else have any thoughts?