Per the 20th amendment[1], the new president's term begins immediately after the old president's term ends. This means that Obama became president at 12:00, even without being sworn in. He couldn't "enter on the execution of his office" until he was sworn in, but he was nonetheless president.
The argument is that Rice was president due to the succession laws. I understand that this succession does not require swearing in. Then, as soon as Biden did swear in, at 12:01, he became acting President.
(6) Neither Nancy Pelosi nor Robert Byrd actually resigned their seats in the Congress. Thus, neither of them qualified to become Acting President under the Presidential Succession Act. Plus, interbranch appointments might be unconstitutional anyhow. See Akhil Reed Amar and Vikram David Amar, Is the Presidential Succession Law Constitutional?, 48 Stan. L. Rev. 113 (1995); but see Howard Wasserman, Structural Principles and Presidential Succession, 90 Ky. L.J. 345 (2002).
furthermore, to the parent comment:
I suppose the obvious counterargument is that Secretary Rice also never took the Oath prescribed in Art. II, Sec. 1, cl. 8, and thus was no more qualified than Barack Obama or Joe Biden to act as President at 12:00 noon. But if Secretary Rice was not President from noon to 12:01, then who was?
Verdict: today is an interesting meatspace reminder to check your edge cases.
Actually, it's also a reminder that, like plentyoffish, a working system can ignore edge cases and be incredibly successful for unrelated reasons, and only a few people will complain about the failure at the edge. :)