Despite the impressive capabilities of recent Large Language Models (LLMs) to generate human-like text, their ability to produce contextually appropriate content for specific communicative situations is still a matter of debate. This issue is particularly crucial when LLMs are employed as assistants to help solve tasks or achieve goals within a given conversational domain. In such scenarios, the assistant is expected to access specific knowledge (e.g., a database of restaurants, a calendar of appointments) that is not directly accessible to the user and must be consistently utilised to accomplish the task.In this paper, we conduct experiments to evaluate the trustworthiness of automatic assistants in task-oriented dialogues. Our findings indicate that state-of-the-art open-source LLMs still face significant challenges in maintaining logical consistency with a knowledge base of facts, highlighting the need for further advancements in this area.