See, I agree with the first two paragraphs, but I don't think the third automatically follows.
Alignments are guidelines. It's a spectrum. In the campaign in question, the two characters who argued the most about the issue was the LG paladin and the other LG figher. Both firmly within their alignment, but just different takes on the situation.
I don't see how a party split automatically happens with this. Morality isn't black and white, and I think the best paladins are those that recognize that fact and try to strive for good anyway. It often result sin conflict, but it doesn't automatically have to be earth shattering... But then again, I like my campaigns with some murk and grey in them.