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V404 Cyg, Cyg X-3, V4641 Sgr, and GRS 1915+105 are among the brightest X-ray binaries and display complex behavior in their multiwavelength emission. Apart from Cyg X-3, the other three sources have large accretion disks, and there is evidence of a high orbital inclination. Therefore, any large scale geometrical change in the accretion disk can cause local obscuration events. On the other hand, Cyg X-3 orbits its Wolf-Rayet companion star inside the heavy stellar wind obscuring the X-ray source. We study here whether the peculiar X-ray spectra observed from all four sources can be explained by local obscuration events. We fit the source spectra with two physically motivated models describing either a scenario where all the intrinsic emission is reprocessed in the surrounding matter or where the emitter is surrounded by a thick torus with variable opening angle. We show that the X-ray spectra during specific times are similar in all four sources likely arising from the high-density environments where they are embedded. The fitted models suggest that a low-luminosity phase preceding an intense flaring episode in the 2015 outburst of V404 Cyg is heavily obscured, but intrinsically very bright (super-Eddington) accretion state. Similar spectral evolution to that of V404 Cyg is observed from the recent, unusually low-luminosity state of GRS 1915+105. The modeling results point to a geometry change in the (outflowing) obscuring matter in V404 Cyg and GRS 1915+105, which is also linked to the radio (jet) evolution. All sources display obscured X-ray emission but with different intrinsic luminosities which points towards different factors causing the obscuration. This work highlights the importance of taking into account the reprocessing of the X-ray emission in the surrounding medium in the modeling of the X-ray spectra that may well take place in other sources as well.