How to make Illustrator not to lie about colors?

Question

Here is the fragment of red area, which is said by Illustrator as being #840608 (upper green marker). But actually, as reported by screen inspecting application, the color is #9C0D01 (lower gree marker).

Later, when I starting to export image for web, the color is becoming #B70F00

Finally it becomes #9B0203 in we browser:

How professional program can be so inaccurate with colors? If this is a result of some feature (the usability of one is of high doubt) the how is it possible to disable it totally?

So, I need color code conserve full way from drawing to web.

UPDATE

I am measuring screen colors with Instant Eyedropper utility. It works exact with web browsers:

jsfiddle link: http://jsfiddle.net/dimskraft/VT8T4/

UPDATE 2

Illustrator file: https://drive.google.com/file/d/0By8pZ9a2478YNzVBejVsM21fWFU/edit?usp=sharing

Answer 1

Okay... here's your issue.

You started a new Illustrator document in CMYK mode. Then at some point later, you switched the Document Color Mode to RGB. This causes the document to still use the color settings for CMYK. In fact, when you simply switch color modes on the fly many things within Illustrator stick to the old color mode - the color profiles, the libraries (swatches, symbols, brushes, etc.).

When creating a new file in Illustrator you need to start with the color mode needed for output in order to maintain color. This is especially true for RGB since the CMYK gamut is so much smaller. Switching color modes mid-document will often have unexplained results where color is concerned.

How do I know this..... download your Illustrator file and open it.

• The Swatch Panel is loaded with CMYK color even though to document color mode is RGB. That doesn't happen if you start with an RGB document.

• Copy your red button. Create a new RGB document and Paste. The color is #9a0203 (which is as close as CMYK can get to #840608).

Now, in an RGB Document set the color to #840608 and it will match your browser colors.