Yes, America still leads in manufacturing. Does it matter to most people? No. As this article points out, accurately, China mainly has taken the lead in "labor-intensive" goods. If people are mostly buying Chinese goods and can't find work making these low-end goods, they have legitimate reason to believe that we've fallen behind.
Our lead in highend products is all well and good for owners of capital, but the sentiments expressed in song and popular culture are still valid.