Simplest extensions of single particle dynamics in a momentum conserving active fluid-an active suspension of two colloidal particles or a single particle confined by a wall-exhibit strong departures from Boltzmann behavior, resulting in either a breakdown of an effective temperature description or a steady state with nonzero entropy production rate. This is a consequence of hydrodynamic interactions that introduce multiplicative noise in the stochastic description of particle positions. This results in fluctuation-induced interactions that depend on distance as a power law. We find that the dynamics of activated colloids in a passive fluid, with stochastic forcing localized on the particle, is different from that of passive colloids in an active fluctuating fluid.