The European Space Agency's (ESA) Rosetta mission has returned a vast data set of measurements of the inner gas coma of comet 67/Churyumov-Gerasimenko. These measurements have been used by different groups to determine the distribution of the gas sources at the nucleus surface. The solutions that have been found differ from each other substantially and illustrate the degeneracy of this issue. It is the aim of this work to explore the limitations that current gas models have in linking the coma measurements to the surface. In particular, we discuss the sensitivity of Rosetta's ROSINA/COPS, VIRTIS, and MIRO instruments to differentiate between vastly different spatial distributions of the gas emission from the surface. We have applied a state of the art 3D DSMC gas dynamics code to simulate the inner gas coma of different models that vary in the fraction of the surface that contains ice and in different sizes of active patches. These different distributions result in jet interactions that differ in their dynamical behaviour. We have then produced synthetic measurements of Rosetta's gas instruments. By comparing the different models we probe the limitations of the different instruments to variations in the emission distribution. We have found that ROSINA/COPS measurements by themselves cannot detect the differences in our models. While ROSINA/COPS measurements are important to constrain the regional inhomogeneities of the gas emission, they can by themselves not determine the surface-emission distribution of the gas sources to a spatial accuracy of better than a few hundred metres (≃400 m ~50 MFP). Any solutions fitting the ROSINA/COPS measurements is hence fundamentally degenerate, be it through a forward or inverse model. Only other instruments with complementary measurements can potentially lift this degeneracy as we show here for VIRTIS and MIRO. In particular, we find that MIRO is the only instrument that can distinguish between most of our models. Finally, as a by-product, we have explored the effect of our activity distributions on lateral flow at the surface that may be responsible for some of the observed aeolian features.