"Well" and "good" as predicate adjectives are both completely fine grammatically. Al's lyrics there are just telling people not to confuse the separate idiomati

"Well" and "good" as predicate adjectives are both completely fine grammatically. Al's lyrics there are just telling people not to confuse the separate idiomatic meanings of "doing well" and "doing good". For "I am well/good", I think what you have in mind is that there's a classic nitpick over which refers to health and which doesn't. Some people claim that "I am well" means the speaker is healthy, and object to using it otherwise or to using "good" with the same meaning (e.g. James Brown's "I feel good"). But I think most sources dismiss this claim as outdated or just confused, and consider both usages acceptable.