The oxygen triple-isotope composition (Δ′17O = δ′17O - θ × δ′18O) of tropospheric O2 is an important parameter used in mass-balance proxy estimates of gross oxygen productivity in the modern ocean and the global biosphere. We created a chemical reaction network box model of the Δ′17O budget of tropospheric O2 to examine the key controls on the oxygen triple-isotope composition of tropospheric O2 (Δ′17O O2, trop). Our model is composed of four boxes: the stratosphere, the troposphere, the terrestrial biosphere/hydrosphere, and the marine biosphere/hydrosphere. We find that including an O2 consumption flux via Mehler-like reactions in marine cyanobacteria equal to between 40 and 50% of marine gross oxygen productivity resolves three issues at once: 1) interlaboratory disagreements on the oxygen triple-isotope signature of tropospheric O2 in the present day, 2) the incompatibility of model predictions of Δ′17O O2, trop with corresponding air observations in two laboratory reference frames, and 3) puzzling discrepancies between concurrently measured Δ′17O-gross oxygen productivity and 14C-net carbon productivity rates in the ocean. We also discuss how variations in the extent of Mehler-like reactions complicate Δ′17O-based interpretations of global gross oxygen productivity since the Last Glacial Maximum and propose a series of experiments to test our hypothesized large flux of O2 being consumed by Mehler-like reactions in the global O2 budget. Fundamentally, this work questions what variations in the Δ′17O of O2 indicate about global biogeochemical cycling.