In visual crowding, the perception of a target deteriorates in the presence of nearby flankers. Traditionally, target-flanker interactions have been considered as local, mostly deleterious, low-level, and feature specific, occurring when information is pooled along the visual processing hierarchy. Recently, a vast literature of high-level effects in crowding (grouping effects and face-holistic crowding in particular) led to a different understanding of crowding, as a global, complex, and multilevel phenomenon that cannot be captured or explained by simple pooling models. It was recently argued that these high-level effects may still be captured by more sophisticated pooling models, such as the Texture Tiling model (TTM). Unlike simple pooling models, the high-dimensional pooling stage of the TTM preserves rich information about a crowded stimulus and, in principle, this information may be sufficient to drive high-level and global aspects of crowding. In addition, it was proposed that grouping effects in crowding may be explained by post-perceptual target cueing. Here, we extensively tested the predictions of the TTM on the results of six different studies that highlighted high-level effects in crowding. Our results show that the TTM cannot explain any of these high-level effects, and that the behavior of the model is equivalent to a simple pooling model. In addition, we show that grouping effects in crowding cannot be predicted by post-perceptual factors, such as target cueing. Taken together, these results reinforce once more the idea that complex target-flanker interactions determine crowding and that crowding occurs at multiple levels of the visual hierarchy.