Why use LNAs in a noise generator?
Most noise in opamps, like thermal noise and Schottky noise ("shot" noise) is white, i.e. has a flat spectrum, but for instance flicker noise (aka 1/f noise) isn't. The MAX2650 will have lower noise overall, both white and colored.

But even if the overall noise is close to white there may be other reasons not to choose an opamp, and they are not always technical.
Application notes by manufacturers are not just to offer the customer a service. They're also/mainly a promotion vehicle, to place the manufacturer's products in the spotlights. Maybe the marketing guys at Maxim thought that the MAX2650 didn't get enough attention.  



further reading:
This TI document tells you more about noise in opamps.