Our interest lies in the collisional statistics in an arbitrary interacting fluid, We show that even in the low-density limit and contrary to naive expectation, the number of collisions experienced by a tagged particle in a given time does not obey Poisson law, and that, conversely, the free flight time distribution is not a simple exponential. As an illustration, the hard sphere fluid case is worked out in detail. For this model, we analytically quantify those deviations and successfully compare our predictions against molecular dynamics simulations.