I'm not exactly sure what you're saying here: "The MAF should measure that larger volume of air required to make that dense air." Are you talking about an OEM setup or a blowthrough setup. Meth injection increases power two ways - (1) adding meth allows you to run more boost without pre-detonation, which makes more power and (2) it increases the density of the intake charge by adding mass to it and by cooling it down. Blowthrough accounts for a portion of part (2). Since you are adding more matter to the intake charge (in the form of meth vapor), you're increasing its mass. There is physically more matter in the intake charge than before you added the meth. An OEM MAF can't account for this added matter (mass) because it happens downstream of the MAF. Does this make sense?
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