In more detail, the temperature of the Earth+atmosphere system isn't changed by GHGs (since the absorptivity and thus emissivity isn't changed, and ignoring the role of water vapour in setting emissivity). But the ground temperature may well be.
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The point is, don't try to calculate emissivity by following photons. Use absorptivity + kirchhoff. Infrared emissivity = infrared absorptivity, which is significantly affected by GHGs. And this is (close to) the effective emissivity in S-B
Got it. (Though, ultimately, of course, one would like to understand it from a more local perspective as well).
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Local in what sense? (I don't mean to push you on this and am happy to stop here if you prefer.)
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I just meant what I took you to informally mean by "following photons". Not literally of course, but I meant thinking locally about energy flows, and reconciling with the global picture.
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