Methods for reconstructing sources of inert atmospheric tracers from ground measurements are currently studied, tested, and even implemented (in accident-type radionuclide release backtracking, for retrieval of carbon fluxes). Often the retrieved source exhibits a very strong and unrealistic (therefore unwanted) influence by the observation sites. This problem is shown not to be an intrinsic flaw of the reconstruction methods but rather due to the specifics of the atmospheric dispersion of a tracer, to the location of the receptors and to the expected source location. It is increasingly pronounced as the grid resolution for the source is improved, and we show how this translates mathematically. We rely on the general framework of inversion methods based on the maximum entropy on the mean principle. Those methods are well suited for accident-type tracer release problems. The dependence of the reconstruction on grid resolution is investigated both analytically and numerically, in conjunction with the issue of receptor influence. Two examples of synthetic experiments are given. The first one is a one-dimensional toy model which quantitatively validates the approach. The second one is based on the European Tracer Experiment and agrees well with the results obtained here. Finally, a generalization of the formalism is proposed so as to study the performance of reconstructions when observation and possibly model errors are present.