It is widely assumed that the dominant source of scattering in graphene is charged impurities in a substrate. We have tested this conjecture by studying graphene placed on various substrates and in high-κ media. Unexpectedly, we have found no significant changes in carrier mobility either for different substrates or by using glycerol, ethanol, and water as a top dielectric layer. This suggests that Coulomb impurities are not the scattering mechanism that limits the mean free path attainable for graphene on a substrate.