That all sounds like justification after the event. The US seemed quite content to go it alone, and there was a large popular movement concerned about us joining in. Blair seemed intent on risking the lives of his countrymen (not his own kin mind) for what were obscure reasons once you got...
At any time there are many bad men in charge of countries. Why Iraq ? Why then ? It is the most important of decisions to send your countrymen into war when some will come back in coffins or maimed so a leader better have a sound case and be sure.