Why can't I play with three guitars in The Beatles: Rock Band?

You are correct, The Beatles: Rock Band does not present you with the choice to play two guitars in addition to bass. Our guitar parts were mixed by Giles Martin (Sir George Martin's son) to be an amalgam of all the best guitar parts per song. Keep in mind that later in the Beatles' career they would overdub multiple guitar parts, in addition to other instruments like Moogs, Sitars, Hammond Organs, etc. Because this is aRock Band game, we only have Bass, Guitar, Drums, and Vocals, with the new innovation being support for 3-part vocal harmonies in this game.

And yes, Apple Corps, including the surviving Beatles' and the others' widows all signed off in everything in the game, and were very involved in the whole process.

Thanks so much for your support of our game, and it seems like you're quite a big Beatles fan yourself, so it's great to hear you enjoyed it!