When speech is degraded, word report is higher for semantically coherent sentences (e.g., her new skirt was made of denim) than for anomalous sentences (e.g., her good slope was done in carrot). Such increased intelligibility is often described as resulting from “top–down” processes, reflecting an assumption that higher-level (semantic) neural processes support lower-level (perceptual) mechanisms. We used time-resolved sparse fMRI to test for top–down neural mechanisms, measuring activity while participants heard coherent and anomalous sentences presented in speech envelope/spectrum noise at varying signal-to-noise ratios (SNR). The timing of BOLD responses to more intelligible speech provides evidence of hierarchical organization, with earlier responses in peri-auditory regions of the posterior superior temporal gyrus than in more distant temporal and frontal regions. Despite Sentence content × SNR interactions in the superior temporal gyrus, prefrontal regions respond after auditory/perceptual regions. Although we cannot rule out top–down effects, this pattern is more compatible with a purely feedforward or bottom–up account, in which the results of lower-level perceptual processing are passed to inferior frontal regions. Behavioral and neural evidence that sentence content influences perception of degraded speech does not necessarily imply “top–down” neural processes.