Several sources now claim that the problems that some users have had in accessing Apple's web site is due to a routing problem of Apple's own creation. In particular, one of the links to its servers was temporarily taken down. They assert that as soon as Apple corrects this, access should return to normal. Apple apparently denies that this is the case.
New information suggests that the problem may indeed more likely be due how Sprint and other NSPs handle certain routing requests - combined with Apple sending the request in a way that gets it turned down by Sprint.
At this point, I am reminded of the line from Rising Sun (attributed as a Japanese saying): "Fix the problem, not the blame."