No, you've merely hidden the opening of the file down inside an external utility. The file is still being opened and completely read, you've just managed to introduce a layer of indirection and a fork/exec overhead.

In order to count the number of lines in a file something is going to have to open the file and search through it for end-of-line markers. That is what he meant when said impossible.

(Of course if you were dealing with a file that used fixed-length lines that still were newline terminated you could cheat and do it with stat and /, but for all normal intents and purposes "impossible" is still a reasonable pronouncement. :)