You have read the oracle but, clearly, the BBC would not agree.
The BBC Radio 4 World Tonight "take" on that speech was that Bush had spoken out for European integration. From the interviewer and two guests, we got such choicphrases as "Bush's sudden enthusiasm for further integration in Europe"; that the US "has no better partner than the EU"; and a view that the president was "encouraging a more integrated EU".
A reading of the speech, however, demonstrates that Bush did not once mention the European Union. All his references were to "Europe".
Even Timothy Garton Ash, the arch Europhile, noted this. Cited in several newspapers, his response to the speech was that Bush did not address in his speech the issue of "why it matters for the United States to work with the European Union". "I don't think he will convince many Europeans talking like that ... This is not a breakthrough speech," he said.
Still, hats off to the skill of the Beeb, drawing from the speech something that no one else seems to have noticed.