It's correct, mass is conserved in chemical reactions. The energy doesn't come from converting mass, it comes from rearranging atoms in molecules (which releases chemical energy).

well, to be very technical about it, when you release energy in a chemical reaction, you DO lose a tiny amount of mass, according to E=mc^2. However, the change in mass is very small in a chemical reaction, as the energy released is very small in comparison to the total energy of the system (given by E=mc^2).

Ok, I should have said that matter is conserved, because that's what the author is really talking about (even though he also calls it mass).

In any case, mass can't be converted to energy either because mass already is energy (that's what e = mc^2 means).