Dynamic spectrum sharing (DSS) among multi-operator low Earth orbit (LEO) mega-constellations is essential for coexistence, yet prevailing policies focus almost exclusively on interference mitigation, leaving geographic equity largely unaddressed. This work investigates whether conventional DSS approaches inadvertently exacerbate the rural digital divide. Incorporating Keplerian orbital dynamics, inter-beam co-channel interference, and three real-world constellation geometries (Starlink, OneWeb, Kuiper), we conduct large-scale, 3GPP-compliant non-terrestrial network (NTN) simulations across 20 orbital snapshots spanning 10~minutes of satellite motion. The results uncover a stark and persistent structural bias: SNR-priority scheduling induces a $1.84\times$ mean urban--rural access disparity, with temporal fluctuations reaching $3.9\times$ during favorable interference conditions. Counter-intuitively, increasing system bandwidth amplifies rather than alleviates this gap. To remedy this, we propose FairShare, a lightweight, quota-based framework that enforces geographic fairness. FairShare not only reverses the bias, achieving an affirmative disparity ratio of $Δ_{\text{geo}} = 0.68\times$ with zero variance across all orbital snapshots and interference conditions, but also reduces scheduler runtime by 3.3\%. This demonstrates that algorithmic fairness can be achieved without trading off efficiency or complexity, and that it remains invariant to physical-layer dynamics. Our work provides regulators with both a diagnostic metric for auditing fairness and a practical, enforceable mechanism for equitable spectrum governance in next-generation satellite networks.