That's a gem of marketing blurb! And like all these "true but misplaced" statements, designed to con you out of your $$.
All modern resistors are as low noise as you need. Some older types, consisting of carbon granules pressed together, can exhibit additional noise, simply due to their haphazard construction. But don't worry & save your cash!
Technically, & trying to keep things simple, there are really 2 kinds of noise sources in electronics. Thermal noise, which is related to resistance, and absolute temperature, and semiconductor junction noise in transistors, op-amps, amplifier chips, etc. Semiconductors have resistance too, so they also exhibit thermal noise.
As always, it's down to the skill of the engineer in designing a product to fulfill a function, to minimise noise & distortion in the design. As you can see, thermal noise is related to resistance value. Keep the resistor values low and you minimise noise. Designs which use low impedance (= low resistance) circuitry, such as modern transistor and op-amp based circuits, exhibit less noise than old tube designs.
As for other components, capacitors are remarkably low noise by design. As are transformers, they're just copper wire. (In fact, if you play LPs and have a moving-coil cartridge, a transformer coupler will offer you the lowest noise solution!)
Noise comes from either bad design, a fault, or simply using a piece of equipment outside its designated operating range. IMO, it's really not a problem in 21st century audio!