shalgo: My database has this game as being played at the Chigorin Memorial in 1965.
Yes, 10...c6 is a bad mistake, 10...Bxf3 being necessary.
Interestingly, Nezhmetdinov is not the only strong player to have fallen into this trap. (The others have even less excuse, because they had this game to warn them.)
In 1980, Jose Luis Fernandez Garcia, rated 2390, made the same mistake in a game against Sosonko at Las Palmas.
More recently, in 2008, Samalvuo, rated 2468, played 10...c6? against Nyback in the Finnish team championships, resigning immediately after 11.e5.