The phrase "smelt a rat" means to sense or detect that something is not right. Antonyms for this phrase could include "trusted," "believed," or "accepted." These words suggest a sense of confidence and faith in something, as opposed to the suspicion and doubt indicated by "smelt a rat."
Other possible antonyms include "ignored," "dismissed," or "overlooked." These words convey a deliberate choice to ignore potential warning signs, rather than actively searching for evidence of deception or wrongdoing.
Ultimately, the choice of antonym will depend on the context in which the phrase is being used. However, any antonym will convey a sense of the opposite of "smelling a rat" - whether that is trust, confidence, or simply ignoring potential problems.