Some words have been imported and adapted into English in the past, but I doubt that nước mắm is one of them.
I‘d also say that news outlets should be held to a higher standard than “conversational language.”
But of course, this is all BS. Languages constantly borrow new words. 20 years ago, nobody knew what "pho" or "banh mi" were, but now we all do. We know what it means so much that we leave off the diacritics entirely and nobody is confused. Those diacritics cannot be represented within the framework of English. They're components of a completely different language.
Is it unreasonable that English speakers today will borrow the word "nuoc mam" and use it in normal English conversation? I've already been seeing it on recipe sites for a couple years now. It's about as English as kimchi and ramen. Nobody ever has or ever will look up the hangul or katakana to write about those in an English article, despite them being easy to remember. "nước mắm" is a foreign word written in its language. "Nuoc mam" is the thoroughly transliterated, romanized equivalent. This phenomenon exists in every language on earth that has ever come in contact with another culture. There isn't a higher standard to hold the author to--they're writing how humans do.
It should also be noted that most Vietnamese people don't really care about texting without diacritics. Most text messages are written without diacritics in order to minimize the payload size. It's just about perception when you see foreign western dishes with their diacritics like crème brûlée but see foreign eastern dishes without theirs.