Yes, I missed the minus sign. I’m familiar with the derivations you posted via the grand canonical and canonical ensembles. What bothered me was the Gibbs factor ($1/N!$) if we’re claiming that they are distinguishable. However, your point that that factor actually describes a labelling matter rather than a distinguishability one is very sound, and effectively resolves my conundrum. Thanks.

@naturallyInconsistent, yes, my apologies, I missed the minus sign. The fugacity argument is actually the one I understand. Apologies if that was unclear. I also understand why the Gibbs factor has to come into play when the particles are indistinguishable (in the classical limit). The argument I don’t agree with is the mathematical derivation from the grand canonical ensemble. However, your point offers a fairly satisfying resolution: the Maxwell-Boltzmann statistics are, by definition, the unique ones that coincide with both the Fermi-Dirac and Bose-Einstein ones in the classical limit.