In English I don't think that anyone would say "She assures that" without an indirect object. I would expect "She assures us that" or "She assures them that", etc. In common speech the idea would more likely be stated "She swears that she didn't eat."
Correct, "assure" must be transitive in English while "asegurar" can be transitive or intransitive. One better way to put it while still being very literal is "she maintains." Please all, report the error instead of mentioning it here unless you have something to add to help other learners!