OP thought the expression included neighbor and weigh and were confused about that because it didn't make sense. When, in fact, the expression excludes those words.
ohh, I thought you were making an “a” vs “ay” distinction.
I learned it exactly like them, with neighbor and weigh excluded. It is vague, and your interpretation isn’t wrong though. I’ve included parentheses, if that helps.
I before e, except [(after c) or (as sounding like a, as in neighbor and weigh)]