One method of defining human nature is - more or less empirically - as constituted by those characteristics which human beings share in common. On this basis, reading good fiction can't be one of the constituents of human nature, given how many members of the human species haven't read Proust, Tolstoy, F. Scott Fitzgerald or whoever else it might be.
A conception of human nature can, on the other hand, be an openly normative one, containing an ideal of how to live well. As part of such a conception one might commend reading as making us human or more human. But it is important to note, then, that this is precisely an ideal, held by some people and not by others. It doesn't oblige anybody. For my own part, I think the locution is regrettable that suggests that non-readers aren't as human as readers.
Along those same lines, John Gray quipped that it was strange to see those who call themselves "humanists" spending so much time denigrating what is possibly the defining human activity, religious worship. Do you really love "humanity" just as it is, or do you only love the idea of it, what you imagine to be the potential of it? There's a busybody continuum ranging from mildly annoying to truly dangerous, and while proselytizing book lovers are obviously harmless, it's interesting to see how minor preferences are so quickly and easily shaded with moralistic colors. However, vicarious experience is merely an increased, intensified version of what's already there in the reader's head, good and bad.
As a general rule, I have no great affection for my fellow hairless apes, individually or collectively, but rather than seek to impose my particular vision of the good life on as many of them as possible in the hope of making the world more to my liking, I'd rather spend my time creating that world in miniature and let the rest go about their folly.