The right exposure...

There is so much talks on the internet about high ISO and the right exposure, people often say that there is no noise even at ISO 3200 if you get "the right exposure", but I do not understand what they mean by that.
Yes I know, in low light situation when exposed right at ISO 100 I will get more noise than with ISO 1600 in situations with a lot of light, but we are talking about low light situations.

If I use 35mm lens with F1.8 aperture, 1/100 shutter speed, the light-meter asks for ISO 3200 in order to get the right exposure, there is no alchemy in this, it is very simple.
Click and there it is, a shot with right exposure, but still there is high ISO noise.
I really do not understand what they mean when they say: If you get "the right exposure" there is almost no noise.
I tried to use Exposure Compensation -0.3 or -0.7 in order to get slower shutter speed, but then the image is over-exposed, and I still have noise.

Is that just some placebo, or alchemy they are talking about, or there is some trick I do not understand yet?

Just my ameture humble opinion.
Should be using a tripod in those low light conditions. From what I'm gathering is that at 1/100th shutter speed and 3200 ISO the light is really low.
Bring your ISO down to 800 and set you camera to Aperture Priority and see what shutter speed it comes up with.

Exposure is really a balancing act that takes time and practice to learn.

First of all, when people say that "there is/isn't very much noise", or "the amount of noise is/isn't acceptable" etc., it is very relative (personal, subjective) statement. I made a lot of portraits using a PEN camera (half-frame sensor!) at ISO 1600/2000/3200, JPGs straight out of camera, without a flash, indoors, at some birthday parties or weddings, and people (who were photographed) were quite happy with the results (yes, you can see the pics are "grainy", but the colors are there and the details are preserved too).

The following photo (EXIF included, lens=kit zoom Nikon AF 35-70mm f/3.3-4.5, probably the cheapest lens ever made by Nikon) has been taken under the extremely poor light produced by a single 100W bulb (this isn't a studio, but a dining room with a light bulb hanging from a ceiling) plus a tiny little bit of daylight coming through the window:

Noise has as much to do with the content of the shot as it does with the ISO. Shoot a white wall at ISO 3200 with that D7000 (I had one) and you're going to see plenty of noise. Move a rather busy group of people in front of that white wall, with patterns to distract all those little dots and chances are the noise is less noticeable.

Proper exposure is important, because if you need to manipulate the exposure in post to get it right you're not just going to amplify light, you're amplifying noise. Exposure doesn't limit the noise - that's purely a function of ISO - it's the manipulation of the exposure after the fact. Nail the exposure, compose a good photo, and the noise simply becomes a part of it and not a problem to be dealt with. There are plenty of great photos with plenty of noise, but when you capture the image, THAT is the only thing that people will take away from it (unless they just like criticizing things).

I understand, they are probably talking about later PP...