Current theoretical models for the effect of chaperonins on the folding of encapsulated proteins emphasize the importance of excluded volume effects. Such models predict a stabilization of the native state and strongly accelerated folding rates. However, recent experimental results have shown that, if anything, folding within the chaperonin is actually slowed down relative to unconfined folding. We use a hierarchy of coarse-grained models for the folding of rhodanese within GroEL to address this issue. We show that while indeed a purely repulsive model of GroEL results in the expected acceleration of folding rate, inclusion of a transferable potential between substrate and chaperonin results in a strong slowdown of folding to be as slow as, or slower than, the unconfined case. We have developed and tested a phenomenological theory for this, which shows that folding rates and stability initially increase as a function of substrate:cavity interaction strength, before decreasing again. Lastly, we have used a recently developed model system for protein misfolding, which reveals that encapsulation within GroEL may actually increase the probability of misfolding. This finding is supported by single molecule experiments done on the same system. Taken together, these results support the view that the primary function of chaperonins is to sequester partially folded and misfolded species in order to prevent protein aggregation.