Incorrect, technically. Faults and earthquakes are both results of the release of stored energy (stress) through displacement. However, either can occur without the other. But it's a moot point.
Weakening the strata can result in earthquakes that would never have happened; it is not necessarily as simple as preventing a larger quake down the road. The strata (whether intact or along a dormant fault) may be able to withstand the current stresses (in perpetuity) without yielding, unless it is weakened (e.g. by injection wells).