A major question for the hazard posed by injection-induced seismicity is how large induced earthquakes can be. Are their maximum magnitudes determined by injection parameters or by tectonics? Deterministic limits on induced earthquake magnitudes have been proposed based on the size of the reservoir or the volume of fluid injected. However, if induced earthquakes occur on tectonic faults oriented favorably with respect to the tectonic stress field, then they may be limited only by the regional tectonics and connectivity of the fault network. In this study, we show that the largest magnitudes observed at fluid injection sites are consistent with the sampling statistics of the Gutenberg-Richter distribution for tectonic earthquakes, assuming no upper magnitude bound. The data pass three specific tests: (1) the largest observed earthquake at each site scales with the log of the total number of induced earthquakes, (2) the order of occurrence of the largest event is random within the induced sequence, and (3) the injected volume controls the total number of earthquakes rather than the total seismic moment. All three tests point to an injection control on earthquake nucleation but a tectonic control on earthquake magnitude. Given that the largest observed earthquakes are exactly as large as expected from the sampling statistics, we should not conclude that these are the largest earthquakes possible. Instead, the results imply that induced earthquake magnitudes should be treated with the same maximum magnitude bound that is currently used to treat seismic hazard from tectonic earthquakes.