…which was, of course, what Asa Gray repeatedly stressed vis a vis evolution, as the first “theistic evolutionist” after Darwin.
That said, I’m not actually sure on what basis one can confidently exclude the activity of an intelligent agent inputting information (let’s say God, since we’re discussing “Evolutionary Creation”, in which “God creates through evolution”, rather than ID, in which the issue is merely “evidence for a designer”), except on some theological, rather than scientific, basis.
One has to assume that the hyper-mutations that the immune system undergoes, which are more often than not successful in providing a “fit” for invading pathogens, “would have happened naturally anyway”. But If they’re random, they’re not lawlike and can’t be adequately predicted by science - except statistically. And of course, as Glipsnort himself has helpfully pointed out, we can’t know enough about the causes of individual events in a statistical system to pronounce them random at all.
A limiting example would be statistical studies of mass human behaviours like voting patterns, in which each vote is actually an “intelligent” (with scare quotes given the current US situation) decision. The science can only observe the patterns of outcomes: the individual unrepeatable events are beyond science’s purview.
This is not simply nit-picking in the context of a science-faith discussion, because in classical Christian philosophical theology, the three broad positions possible are:
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Conservationism, which historically has only really been held by Deists, in which God sustains all events in existence without actively influencing them: in this view only is God not actively governing the outcomes providentially.
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Occasionalism, in which God is the sole “true” cause of each event (this had some traction in mediaeval theology, though is far less popular today).
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Concurrentism, in which secondary causes are always actively under the governance of God, in his guiding providence. This has historically been the majority position.
So to claim “information comes into existence all the time without the action of an intelligent agent” is to be assuming, without justifying arguments, a particular philosophy of divine action (or, I suppose, if one were an atheist, assuming a naturalist philosophy in which there is no divine action).
But as you rightly say, a complex system like a coin-toss or an immune system, which exploits what is phenomenologically perceived as “chance”, is itself the evidence of design, the alternative ultimate source being (as Gray said, reminding his readers that the stark choice went back to Aristotle and Epicurus) that chaos can produce order.
One might as well say that the process of human fertilization is so random that it demonstrates God has no active role in creating an individual like you, me, or John the Baptist. Such a conclusion is not scientific, but philosophical and theological - and needs therefore to be justified on those terms rather than smuggled in as “science”.