You're basically saying that, whenever science finds or implies a lack of design, it has strayed into theology. It's going to do that a lot.
No, I'm saying that finding or implying design or the lack of it is subjective, and not scientific. To me, math, physics, chemistry, biology, and even evolution look like design. To another, they might not. But neither of us is one up on the other. That's why science should remain agnostic.
A converse to your statement above imight be: wherever science doesn't find or imply God, we must presume random or nature. There's no need, and the presumption is actually irrelevant to science.
Is a sincere scientist going to accept "random did it" or "nature did it," any more than he would "God did it?" If he sets all three aside, the inquiry proceeds anyway.
What's the downside to an agnostic science?