The first peak of the oxygen-oxygen pair-correlation function (O-O PCF) is a critical measure of the first coordination-shell distances in liquid water. Recently, a discrepancy has been uncovered between diffraction and extended x-ray absorption fine-structure (EXAFS) regarding the height and position of this peak, where EXAFS gives a considerably more well-defined peak at a shorter distance compared to the diffraction results. This discrepancy is here investigated through a novel multiple-data set structure modeling technique, SpecSwap-RMC, based on the reverse Monte Carlo (RMC) method. Fitting simultaneously to both EXAFS and a diffraction-based O-O PCF shows that even though the reported EXAFS results disagree with diffraction, the two techniques can be reconciled by taking into account a strong contribution from the photoelectron scattering focusing effect in EXAFS originating from nearly linear hydrogen bonds. This many-body contribution, which is usually neglected in RMC modeling of EXAFS data, is included in the fits by precomputing and storing EXAFS signals from real-space multiple-scattering calculations on a large number of unique water clusters. On the other hand, fitting also the O-O PCF from diffraction is seen to enhance the amount of structural disorder in the joint fit. Thus, both structures containing nearly linear hydrogen bonds and local structural disorder are important to reproduce diffraction and EXAFS simultaneously. This work also illustrates a few of many possible uses of the SpecSwap-RMC method in modeling disordered materials, particularly for fitting computationally demanding techniques and combining multiple data sets.