This arXiv preprint (abs/2605.26126, May 2026) extends Tweed's 1970s Born-I formalism for electron-impact double ionization of H^-, He, and Li^+ by replacing the Coulomb potential with a q-deformed screened interaction drawn from Tsallis non-extensive statistics. The authors derive modified differential, partial, and total cross sections, showing that q<1 screening damps the high-energy Bethe logarithm while injecting diffraction-like angular oscillations absent in Maxwell-Boltzmann treatments. Calibration uses digitized historical experiments rather than new data collection, with no sample size applicable to this purely theoretical derivation. Limitations include untested assumptions about q-statistics applicability in real plasmas and lack of relativistic or multi-electron corrections. The resulting q-Maxwellian rate coefficients expose a subextensive critical-temperature threshold below which ionization is forbidden, a feature missed in standard models. Related work by Tsallis (J. Stat. Phys. 1988) established the foundational entropy and by Lima et al. (Phys. Rev. E 2002) demonstrated q-effects in fusion-edge plasmas, yet neither addressed atomic ionization cross sections. This preprint's strength lies in linking microscopic form factors to macroscopic rates, but it overlooks potential experimental signatures in laser-produced plasmas where non-extensivity has been inferred from anomalous line ratios.