I think you need to differentiate between what scientists say and what the theory actually says. Many scientists may say that evolution occurs via random variation and natural selection, but the theory itself does not say this. The theory itself says that evolution proceeds via variations that are chosen by natural selection. It doesn't say that these variations are random (although it doesn't say that they are not.) Whether the variations are random or are guided by God in such a way as to appear random is not a scientific question and as such no mention of it should appear in a scientific theory. The reason is that the idea that God guides the variation is not falsifiable. Any potentially falsifying observation could be explained away by invoking the omnipotence of God. When scientists insist that the variation must be random, they are simply injecting their own personal beliefs or reflecting the methodological materialism that science must assume, not stating anything that is implied by the theory of evolution.
I find no fault in your reasoning.