Interestingly, the amount of filliing in a conversation doesn't vary by education/social class (the two will always confound), but the type of filler does, from 'like' to 'actually.' I can't be bothered to find the study (there's quite a few). At the lower end of education/social class, fillers are shorter and used more frequently, higher up, they're longer but let frequent, for instance stepping through the syllable of ac-tual-ly and then pausing. The amount of time spent filling is much the same. Of course, the type of filler you use is a social class cue in itself.
It's very rare for anyone not to have sufficient vocabulary hence the nonsense of that teacher's statement, we all do. The different that education and a lot of reading gives us is access to a lot more synonyms and different ways of saying things.