Now that you mention that I remember that that is what the translation is supposed to be.

Asche zu Asche definitely means Ashes to Ashes. (Ass = Arsch) The lyrics support this semantic: Das Feuer wäscht die Seele rein Und übrig bleibt ein Mundvoll Asche. ~ The fire cleans(clears?) the soul and what remains is a mouthfull of ash.
AFAIK Asche zur Asche is rarely used. Maybe because Asche zu Asche has an all-embracing ring to it since it avoids using "zur = zu der = to the", thus eliminating a specific context.