In semiconductor nanostructures with feature sizes on the order of 100 nm, thermal transport is expected to be well-described by the phonon Boltzmann transport equation (BTE) with diffuse boundary scattering. However, over the past several years there have been reports of anomalously low effective thermal conductivity values in one- and two-dimensional semiconductor nanostructures. In this study, we investigate thermal transport in nanostructured holey silicon membranes using the non-contact optical transient thermal grating (TTG) technique. We compare the experimental results with two ab-initio BTE numerical techniques. We obtain excellent agreement between theory and experiment, indicating that semiclassical Boltzmann transport theory for phonons is adequate for describing room-temperature thermal transport in semiconductor nanostructures with feature sizes on the order of 100 nm.