When discussing arguments for and against the existence of God, it is often assumed that the options are always to reject them or to accept them, and, holding certain other things constant, this is often true. But in reality here, as with other arguments, there is also room for a distinguo, and some discussions of the subject would be greatly improved for considering it. A handy example of what is meant by this is found in the atheist Feuerbach's The Essence of Christianity.
I've talked before about the general features of Feuerbach's view of religion. Feuerbach takes religion to be an expression of a necessary alienation from ourselves. To know ourselves, we have to take our nature as object; religion is taking our nature as object simply. Thus theology on his view reduces the anthropology; what people are doing in religion is treating pictorial representations of human nature as if they were independently existing things. The divine attributes are really human attributes, considered abstractly as if they existed independently of any human being. The divine infinity is a projected reflection of the infinity of human understanding, for instance, treated as if it were standing alone in actual existence. Feuerbach takes the alienation to be necessary for human self-understanding, but the recognition of it as self-alienation to be part of the natural trajectory of human progress. He thus takes his reduction of God to man as a next step up from Protestantism. We see this in a number of ways. For instance, in the Catholic Mass, man is sacrificed to God as real sacrifice to God; in the Protestant Lord's Supper, God gives a gift to man, and it is seen ever more symbolically until we get to Zwingli; the natural next, and Feuerbachian, step is for it to become a gift of man to man, eating and recognizing the work of human hands for human life. So with everything else.
It's clear that on this kind of view evaluation of arguments for the existence of God will have to be split. If we are talking of God as an alienated object separate from human nature, all such arguments would fail. However, since God is alienated human nature, such arguments also succeed when recognized as being about human nature alienated as an object:
At the same time, however, their result is to prove the nature of man. The various proofs of the existence of God are nothing else than various highly interesting forms in which the human nature affirms itself. Thus, for example, the physico-theological proof (or proof from design) is the self-affirmation of the calculated activity of the understanding. Every philosophical system is, in this sense, a proof of the existence of God. (p. 199)
Feuerbach does not, as far as I recall, explicitly recognize it, but the same in reverse would have to go for arguments against the existence of God; they may work against God conceived as separate, but they also show a failure to recognize the features of human nature being alienated into a God so conceived. There's a straightforward sense in which this is an atheistic assessment of the arguments, but it's also not a simple rejection.
We can find similar sorts of distinction on other grounds -- e.g., Iris Murdoch on the ontological argument. They will arise generally on broadly Kantian grounds (due to the division of noumena and phenomena) and on positions that allow some distinction between appearance and reality. And, of course, the reversals are also possible -- one can have a 'reverse Feuerbach' in which all arguments for features of human nature in general are really describing forms of the human reflection of God and so are indirect arguments for the existence of God. Then every philosophical system is indeed, and not just in a sense, a proof of the existence of God. Indeed, it's not difficult to imagine such a thing, given that Feuerbach's own position is often a reversal of Christianity. The closest overall 'reverse Feuerbach' in actual existence would probably be something like a 'High Church' (Evangelical Catholic) Lutheranism, but on the question of the existence of God in particular, the direct reversal would be something a lot like an approach more commonly associated with Reformed Protestantism (Calvinism), namely, presuppositionalism.
How stable all of these distinction-based evaluations are is another question, and probably a complicated one. And, as the previous paragraph might well suggest, they will tend to emphasize one side of the distinction over the other. But this suffices to make clear that they actually exist. And it is worthwhile, even for those who (like myself) take a more straightforward evaluation for such arguments, to remember that they exist.
[Ludwig Feuerbach, The Essence of Christianity, George Eliot, tr., Harper (New York: 1957).]