Sir McCartney only owns the recorded masters, not the copyrights. Those are owned by Sony/ATV (remember that is owned by Michael Jackson and Sony - actually the ATV part, under which the Beatles Catalog falls, is wholly owned by Jackson and leased every 10 years to Sony).
Jackson is an Apple fan and uses Mac personally, however.
EMI/Parlophone owns the recorded masters. ATV/Sony own the publishing rights. McCartney only receives songwriters royalties for Lennon/McCartney songs. He gets nothing for any Beatles songs written by George Harrison or Ringo Starr.
What this means, in essence, is that Paul, Ringo, Yoko Ono, and the estate of George Harrison do not, in any way, control when or if a Beatles song is used; hence the 1980's Nike ads that used 'Revolution', or the 'Come Together' AT&T (?) ads. The only receive royalties for having written the songs. By extension, the use of a Beatles-recorded cover song (like 'Twist and Shout', for instance) is also controlled by EMI, since they own the master; ATV/Sony get nothing in this case because it's not a Beatles-written song. And the Beatles themselves get nothing for the same reason.
This all stems from sale of Northern Songs (Dick James' publishing company, which originally held the publishing rights to Lennon/McCartney songs). John and Paul each owned a 15% share of Northern Songs, but the bulk of the company was sold off to ATV in 1969, with John and Paul following suit shortly thereafter. ATV auctioned the rights off in 1985; Michael Jackson was the successful bidder. Jacko later sold part of his rights to Sony to help pay off his debt.
So, the long and short of it is that Paul has no control over the publishing rights. He simply gets paid when the songs are used. The decision to issue the songs on iTunes would, as far as I can tell, come from two people: first, EMI must approve the use of the masters (which have, in all likelihood, been remastered from the originals); second, Apple (Records) must permit the use of the Beatles name and likeness (i.e. photos of the group members, the famous BeaTles logo, etc).