A recent approach to understanding the mammalian visual system is to show correspondence between the sequential stages of processing in the ventral stream with layers in a deep convolutional neural network (DCNN), providing evidence that visual information is processed hierarchically, with successive stages containing ever higher-level information. However, correspondence is usually defined as shared variance between brain region and model layer. We propose that task-relevant variance is a stricter test: If a DCNN layer corresponds to a brain region, then substituting the model’s activity with brain activity should successfully drive the model’s object recognition decision. Using this approach on three datasets (human fMRI and macaque neuron firing rates) we found that in contrast to the hierarchical view, all ventral stream regions corresponded best to later model layers. That is, all regions contain high-level information about object category. We hypothesised that this is due to recurrent connections propagating high-level visual information from later regions back to early regions, in contrast to the exclusively feed-forward connectivity of DCNNs. Using task-relevant correspondence with a late DCNN layer akin to a tracer, we used Granger causal modelling to show late-DCNN correspondence in IT drives correspondence in V4. Our analysis suggests, effectively, that no ventral stream region can be appropriately characterised as ‘early’ beyond 70ms after stimulus presentation, challenging hierarchical models. More broadly, we ask what it means for a model component and brain region to correspond: beyond quantifying shared variance, we must consider the functional role in the computation. We also demonstrate that using a DCNN to decode high-level conceptual information from ventral stream produces a general mapping from brain to model activation space, which generalises to novel classes held-out from training data. This suggests future possibilities for brain-machine interface with high-level conceptual information, beyond current designs that interface with the sensorimotor periphery.