How does negative feedback reduce noise?
Feedback reduces all types of errors introduced by block "G" in the schematic above, including noise.

However, all feedback does is minimize \$ \theta_e \$ which does not reduce noise or other kinds of errors (offset...) from the input stage (represented as a substractor on the schematic).

This has practical applications in opamps for example, if you want to pay more for low-noise transistors, they have to go in the input stage. 1/f noise in the rest of the circuit will be reduced by feedback.

So when saying "feedback improves characteristic X" it is important to keep in mind what is "characteristic X" and to what part of the circuit it applies.