So we'll strike "cold" virus from the original sentence and insert "retro virus". Like this:
God did not "design" retro virus DNA into human/primate DNA. Viruses do that on their own. Every time you get a [retro virus] is proof that they do.
Now it's your turn to show evidence that God "designed" broken retro virus DNA into primate and human DNA in a way that looks identical to a common ancestor, just to fool us.
Then you need to get your concept through Occam's razor as to why it's a better explanation that an unseen, unmeasureable, intellegence is messing with us via retrovirus DNA rather than it was just a simple infection in a common ancestor millions of years ago.
Even your correction, whilst better, is not accurate and indicates a fundamental lack of understanding the most basic biological principles.