Question About Computer Evaluations

I've been studying the Man vs. Machine match between GM Lenderman and Komodo, and there's something that troubles me.

It's suspicious on the surface that you can reduce the advantages and disadvantages of a position into a given number. I mean, when we humans look at a position, we usually evaluate it in terms of strengths and weaknesses and whether we would rather play black or white, right?

A computer performs the same evaluation and outputs a number that represents the stronger side as a multiple of "extra pawns possessed," or something -- using that as a currency.

It would be odd for a human to put such a number on a position, but when the computer does so, we all trust its meaningfulness implicitly. Is this correct?

That's a fine question on its own, but I have a more technical one.

In Game 3 of the Lenderman / Komodo match, at a certain moment toward the end white's position was collapsing, and with each move the analysis tipped further in black's favor -- from -1.5 to -2.5 to -4, etc.

But if that number represented all the possibilities in that position, shouldn't that mean that there'd be SOME move that would maintain that analysis as it is?

Or, in other words, if my computer tells me that my position is -1.5, and I make the best move on the board, and it drops to -2.5, wasn't I REALLY at -2.5 in the first place?

Perhaps someone can explain this to me.