If you are given a Sudoku grid to solve (such as in a newspaper or a puzzle book) and there is more than one solution to it, then you've gotten a decidedly inferior offering, some would say an invalid one (as would I).

I'm at a loss as to how you got from "only considered to be correct" to "all possible starting states". And proving that, for example, a standard grid with only a single digit filled in can be "solved" in more than one way is trivial.

But I would disagree with lidden if that was an implied assertion that a program for solving a Sudoku need not be able to deal with such flawed offerings. Indeed, it should probably be able to produce at least two solutions so that you can include them when you write to the source of the puzzle to complain. :)