From personal accounts, ones I've only read about, it seems that sensitivity to things like MSG, ingested orally, are completely possible. But the reactions are small enough to never require any medical attention or further study. No anaphylaxis for instance. Anyhow, since the reactions aren't large enough to be measured in an acute way there is no allergy. However when lay-people speak about how they have reactions to something they eat you might often encounter them using the term allergy in a sense that doesn't require caring a steroid injectable.
It might be MSG causing a headache or eating too much salt in a single meal but either way the symptoms are avoided by elimination of that from their diet. No deaths, no acute reactions, no more study needed. It hurts when you do that? Stop doing it.
In essence they have proved through research that MSG causes no allergic reactions. https://www.ncbi.nlm.nih.gov/pubmed/19389112/ But they can't say there are no reactions at all. (last paragraph http://www.mayoclinic.org/healthy-lifestyle/nutrition-and-he...)
It might be MSG causing a headache or eating too much salt in a single meal but either way the symptoms are avoided by elimination of that from their diet. No deaths, no acute reactions, no more study needed. It hurts when you do that? Stop doing it.