I can give you an example where the literal interpretation is not true to fact because it is not the intended meaning. “I’m starving.” I’m starving, if taken figuratively to mean I’m hungry, is not necessarily not true to fact by nature of it being a figurative expression. It is a truthful way describe being hungry in English that all native speakers will understand as hyperbole in all typical contexts.
The literal interpretation of “I am a single mother” is that I am not married and have children. That is the literal meaning, but it is also not true to fact, because I am married. I told a friend this week “I am a single mother” because my husband is traveling and I am parenting alone. My friend understood my figurative meaning as being a true statement about my situation this week, even though if she took it literally, it would not be true.