What's this about bromide? It was suggested as a word representing stating the obvious. I'm not familiar with this expression. English is not my first language.
Potassium bromide was widely used as a sedative in the 19th/early 20th century. Hence, the term bromide came to be used to mean, not so much 'stating the obvious' as 'a trite statement intended to reassure people and make them feel good'.