That's what I was saying here. You usually are better off using a higher ISO to avoid a noisy image, rather than using a lower one and raising the brightness in post. In other words, a high ISO value is usually adding less noise than a lower one.You can't really say that as a rule because each camera has different ISO amplification quirks. Sometimes the hardware amp in the camera is better / lower noise than trying the same amplification in post-proc software for a given ISO.
The main source of noise in images shot with modern sensor is photon shot noise, which is a property of light itself and has absolutely nothing to do with the sensor. It purely depends on the amount of photons you gather - which is determined by the f/number and shutter speed. Read noise (what the camera introduces) plays a part, but it is not as significant anymore. That's why we don't see huge improvements between sensor generations anymore. The shot noise is a physical limit to how good it can get, and as the distance to the theoretical perfection shrinks, it gets harder and harder to push forward.Shutter and aperture don't introduce any noise. How can they? They are purely mechanical functions. Noise arises from quantum and thermal effects in the sensor plus downstream processing.