The Father Turned His Face Away?

One of my favorite songs says it's so, but that particular line has always bothered me a little. Did the Father really turn his face away from the Son?

I know that Christ cries out from the cross, "My God, my God, why have you forsaken me?" Have you noticed, though, that in the same messianic psalm that Christ is quoting, it says this:

For he has not despised or abhorred
the affliction of the afflicted,
and he has not hidden his face from him,
but has heard, when he cried to him. (Psalm 22:24 ESV)

So, what do you think? Face turned away or not? Does it matter?

[Updated to add this question I touched on originally in the comments: When we say that God turned his face away are we thinking about the Father and the Son as more separate than these two persons of the Trinity really are?]