It's a politician's speech, so you can't expect great clarity of analysis. But the "billboard paragraph" is clear enough:
We should be solid but not slavish in our friendship with America.
It all comes down to a sense of confidence.
Your long-standing friend will tell you the truth, confident that the friendship will survive.
In a sense, talk of "friendship" in international politics is dubious. States cannot be friends -- they are instrumentalities of coercion, sometimes justified coercion, but coercion. But if we have to engage in this cant, we should at least acknowledge that a friend is not someone who defers to your judgment and power, but a person with whom you have a relationship of reciprocal loyalty.
Cameron sensibly excludes democratization, but not the prevention of genocide, from the possible justifications for war. He also specifically criticizes Guanatamo Bay, which the Bush administration is unlikely to forgive. The peroration invokes Gladstone, which is a bit odd for a Tory leader, and a bit frustrating for those of us who share Disraeli's opinion of Gladstone's romanticism, if not Disraeli's own imperial ambitions.
In any event, Cameron has pointed to how a genuinely conservative Anglophone leader should regard America and the world. It is certainly a great improvement over the degraded Asperite bellowing that passes for right-wing thought in this country.