Wolf – Actually Chazal answered your question: “Mutav Sheh Lomaid Torah V’osek B’mitzovs shelo L’shma -she metoch shelolisma Boh lishma.” (It’s good to learn Torah and do Mitzvos without the proper intention, because even so eventually you’ll come to do them with the proper intention.) Your OP is a classic example.
My pet peeve is when people do things and talk it into themselves they are only doing it for good, but something evil comes out of it. Then they say- that outcome had nothing to do with them. Even if they truly meant it L’shem Shomayim- it’s even worse than the catergory of a Mitzvah Haboh B’aveira!