(S3 -- see footnote) Classes don't "implement" anything in R the way they would in other languages. They are labels that tell dispatch functions how to deal with an object. A tibble is internally a data frame. The last example in my post makes this exactly clear.

The other OO systems in R do act closer to traditional classes, but all the tidyverse stuff is S3.

(But the OP was correct in another sense related to the example narrowly!)