The oft repeated phrase from both of these professors was that "the basic unit of language is not the word, but the phrase". In other words, traditional language learning (and Biblical hermeneutics) focused on learning a bunch of words and learning grammar to know how to fit these words together, but in fact speakers think in whole phrases, with maybe swappable words which can be passed in and out. "I want some [water]" is a fixed standard phrase, and children learn it as a whole. While mastering such basic phrases childrean also learn to play with them, and it is simple enough to swap some other need for [water], or add in some sort of negative. As they play and make mistakes, they eventually morph the fixed good phrase into another good phrase: "I [no] want some [sandwich]" --> "I don't want a sandwich". Traditionally, hermeneutics textbooks loved the study of etymology, but these professors also emphasized that the meaning of a word derives from its context, and from contemporary usage far more than the history of the word. Example, most people who use "glamour" don't have a clue that it means "magic". This might seem to be a slight digression from the structural approach, but Moisés Silva applied the structural approach to the study of words in his 1983 book, Biblical Words and their Meaning.
These professors did not discourage studying a lot of vocabulary and grammar, but their use of the structural approach came into play more when studying a text (because, of course, they were teaching hermeneutics, i.e. interpretation). They encouraged us to read whole sections first, look for the larger meaning of the whole, before drilling down to asking why a specific word is used here instead of another, or why this particular tense was chosen over another. And they strongly implied that spending time reading the biblical texts was more useful for learning the languages than spending time flipping vocabulary cards, given a basic core of knowledge from first year Greek or Hebrew.
This structural approach sounds a lot like the "Lexical Approach", except that the structural approach is much older, dating back to the work of the Swiss linguist Ferdinand de Saussure (according to my search in Wikipedia just now), who died in 1913. So, add to what Emk wrote about common patterns in education the fact that the "brilliant professor" who "gets good results" has probably picked up the ideas from somewhere but doesn't know where, so then their followers begin to attribute the "new" approach to that professor's genius and a movement is born.