Several hundred ring-like structures seen at 8μm in the Spitzer GLIMPSE surveys share a uniform morphology: the shell thickness Δ R is a nearly constant fraction of the outer radius R, Δ R/R∼0.3, across a factor of 40 in size and all exciting spectral types. This invariance is unexplained. We ask what sets this thickness and whether its near-constancy is physical or a measurement artifact. We derive analytic constraints on the location, temperature, and heating of the emitting grains, and confront the predicted scaling with radius against the GLIMPSE I and II catalogs (591 objects, 91 with kinematic distances). Grains in radiative equilibrium at the observed radii reach only 20-35 K and fall short of the required 8μm emissivity by more than 20 orders of magnitude; the emission must come from stochastically heated PAHs and very small grains, and therefore from the photon-dominated region, where the ring width is the far-ultraviolet penetration depth. This gives Δ R/R=A_V^(rm PDR)/A_V^(rm cloud), independent of radius; a swept-up shell instead predicts Δ R/R∝(R/R_S)^(3/2), with R_S the initial Strömgren radius. We find a pronounced angular-resolution systematic that inflates the ratio for the smallest bubbles; once this is accounted for, Δ R/R=0.217, with a residual dependence on physical radius of 0.03±0.05, consistent with zero. A fixed ambient density is excluded at 20σ, the swept-up shell at 9-28σ. The implied columns are N_(rm cloud)≈8.7×10²¹ cm⁻² with only 0.112 dex of scatter. The near-universal appearance of mid-infrared bubbles follows from the ratio of two nearly invariant column densities – the dust-opacity-fixed far-ultraviolet shielding column and the Larson-like column of the parent molecular cloud – and requires no reference to stellar winds.