The real position is that east Asia - the audience Mr Christopher was addressing - needs the US, and America is the prime focus of the region's foreign policy rather than the other way round. East Asia is not only dependent on trade surpluses with the US for its economic growth, but relies on Washington for its security. Because the region's nations are wary of each other, the US has found itself at the hub of a wheel whose spokes are bilateral security arrangements.
The Secretary of State emphasised that American trade with Asia is one and a half times greater than with Europe, but tactfully did not comment on the imbalances in the relationship. Nor did he point out that the web of security links binding the US to Europe, such as Nato and the Conference on Security and Co-operation in Europe (CSCE), has no parallel in Asia.
Gerald Segal, of the International Institute of Strategic Studies in London, said: 'The US has fundamental interests in Asia, but they are economic. Culturally, its instincts remain European, as shown by the recent clash of views at the Vienna summit on human rights, where the Europeans and Americans were on one side, and most of the Asians on the other.'
President Clinton has proposed that as a step towards changing this, a ministerial meeting of the four-year- old Asia-Pacific Economic Co-operation (Apec) body in Seattle in November should be upgraded to a summit of government leaders. The aim would be to create 'a comparable sense of familiarity and friendship' to the one between the US and Europe, but the response from some potential participants has shown how far there is to go.
China, for example, is receptive to the idea, as long as Hong Kong and Taiwan are kept out. Malaysia's maverick Prime Minister, Mahathir Mohamed, will stay away.
The US, according to Mr Christopher, considers Apec the 'cornerstone' of its relations with the Asia- Pacific region. But the organisation has no brief to deal with the security questions which loom over east Asia, such as North Korea's nuclear programme and China's increased military spending in support of its ambitions in the South China Sea. Japan has begun warning that it might have to reconsider its non-nuclear stance if the threat from its neighbours grows unchecked.
East Asia faces unresolved issues dating back to the Second World War. The incoming 'non-Liberal Democratic Party' coalition in Japan hopes to make a new start by making a comprehensive apology for Japanese aggression earlier this century, but Peking recently told Tokyo that it opposed Japanese participation in international peace-keeping operations, and the outgoing LDP government has just outlined plans to strengthen the armed forces. Military spending is also rising in south-east Asia. An attempt to confront these issues is at last being made by the Association of South-East Asian Nations, founded 26 years ago to keep Communism at bay and promote capitalism. Its annual meeting in Singapore - the event that drew Mr Christopher, along with his counterparts from China and Russia - decided to set up a regional forum to tackle political and security questions. Apart from Asean's six members, it will include the group's main trading partners and the other countries with military strength in Asia and the Pacific: Russia, China and Vietnam.
Dr Segal put the initiative in perspective: 'The main test is whether it can move beyond rhetoric towards transparency on security issues, such as arms transfers, or inspections of troop manoeuvres,' he said. 'This is nowhere near another Nato, nor even another CSCE. We might be seeing the beginning of a Helsinki process.'
The region is unlikely to make early progress in disentangling the claims by six countries to the Spratly islands, in the South China Sea. The two Koreas are not expected to be reunited without any disruption, and the rise of China may prove the biggest problem of all.
Asians are uncomfortably aware that Mr Clinton was elected to deal above all with the US budget deficit and that he can be expected to seek savings on US military commitments around the world. Given the dangers that exist in east Asia, they will hope to persuade him against any precipitate attempts to make them responsible for their own security.
It was a message that some might have been hoping to give to Mr Christopher before his early departure from Singapore. If the Seattle meeting goes ahead, they are sure to take the opportunity to make their case directly to his superior.