I recently ate a bag of potato chips made by FoodShouldTasteGood, Inc.. Their motto (as printed on that bag under their name) was, "It’s our name. It’s our brand. It’s our motto." Now, either the antecedents for those three it’s are different — which seems implausible — or their motto is lying in its final sentence. It’s all very complicated.
Seth Schoen reminded me of a somewhat similar issue with the United States’ national anthem, The Star Spangled Banner. The final stanza includes the line, "And this be our motto—’In God is our trust.’" This is not and has never been the U.S. motto. In fact, the U.S. had no motto at all until 1956 when "In God We Trust" — which is very similar, but not quite the same — became official.
It seems that nobody is quite sure where "In God We Trust" came from but there is some speculation that it originated in the anthem itself. Presumably, it became the motto because lawmakers thought it sounded good in the song and not because the U.S. government failed while trying to "correct" the embarrassing incorrect line in its anthem.