I honestly don't understand the confusion over this statement. It's just a corollary of Occam's razor. To understand either, one must first accept that scientific inquiry doesn't really search for the truth, but for explanations that model the truth, in ever increasing levels of accuracy.
Occam's razor, "entities [of explanation, assumption, etc.] should not be multiplied beyond necessity", is usually simplified as "the simplest explanation is the best" but is better phrased as "the simplest explanation
that encompasses everything in the observation is the best." As a Philosophy professor once explained it in a class I attended many years ago, you can explain the operation of a florescent light by saying invisible and intangible mice are carrying the electrons back and forth in the tube at very, very high speeds - but a better explanation eliminates the mice altogether. It doesn't absolutely mean the mice don't exist, it just means you can make an adequate explanation without even having to consider the mice.
We used to think that Newton's laws explained everything about motion and gravity, and they still work pretty well in most everyday applications. But Einstein showed that you actually needed a more complex model to explain some things that don't fit in with Newton's laws. Before Einstein, the discrepancies between actual planetary orbits and the calculated orbits using only Newtonian physics were tentatively explained in a number of different ways, often including as-yet undiscovered planets that affected the orbits of the known ones. This makes good sense in the context of Newtonian physics - but those planets don't exist. Einstein made
extraordinary claims about the nature of time and space, and scientific experimentation showed that he was "right", in that those claims made for a better explanation, even though the explanation itself was now more extraordinary - that is, more complex.
Yes "extraordinary" is a subjective thing. But the saying associated with Sagan is simply describing - in a very simple way - the very nature of empirical science. You can claim, for example, that you saw an airplane fly overhead, and a reasonable scientist would probably take your word for it. You can claim you saw metallic, disc-shaped object fly by at close range, and a reasonable scientist would ask for more information, and probably more proof - photos if possible. You can claim that intelligent insectoids from Glarma-12 flew around your head in a flying saucer that used antigravity power, and that same scientist would have no way of evaluating the claim - even though some people would say it's not that different from the previous one - since
- There are no known intelligent insectoids.
- There is no place known commonly as Glarma-12.
- There is no known process of actual antigravity, or even an agreed-upon definition.
That doesn't mean that intelligent insectoids from Glarma-12
didn't fly around your head in a flying saucer that used antigravity power, it just means that there's no way of proving it
scientifically at the current time.