The effect of solvation on the conformation of a dense one-component fluid composed of freely jointed repulsive trimers is calculated theoretically and compared to results from computer simulation. All monomers in the fluid interact with one another via the purely repulsive, shifted-truncated Lennard-Jones potential. We are able to confirm an earlier suggestion that when the conformation of nonpolar flexible molecules is calculated with a site-site solvation potential and the reference interaction site model (RISM) theory, better results are obtained with the recently derived Percus-Yevick (PY) style solvation potential than the hypernetted-chain (HNC) style or Gaussian-fluctuation solvation potential. Interestingly, although RISM-based theory predicts well the general shape of the probability distribution of trimer conformations, it cannot recover a small feature observed in the simulations and expected on simple physical grounds. At high density, there are three preferred conformations of the trimer, corresponding to the three ways in which a flexible trimer can be fitted into a dense fluid with locally hexagonally close-packed (hcp) symmetry. RISM-based theories predict a preference for only two conformations of the trimer. To predict the preference for all three conformations, information about three-site correlations in the fluid must be incorporated into the theory. We present a theory that includes this information and is thereby capable of reproducing the results of our simulations.