Using Illustrator CS6, how to preserve drawn colors when Save For Web to PNG?

Question

Using Illustrator CS6 on Mac OSX 10.9.1:
step 1. I open a new file for Web profile.
step 2. I verify that File > Document Color Mode is RGB.
step 3. I draw a square and set it's color to 0,103,197 (decimal).
step 4. I click File > Save For Web
step 5. In the popup that opens, I set to PNG-24, and verify the option Convert To sRGB is not selected.
step 6. Using the Mac's DigitalColorMeter, I observe the color is 0,109,191 in the Save For Web popup. If I save it, then open the saved PNG file, it's color is also 0,109,191.
How to do this so the colors don't change?
step 7. I close Save For Web popup.
step 8. I verify Edit > Color Settings for Working Spaces is set to Monitor RGB, and that the Color Management Policies for RGB is off.
step 9. I verify Edit > Assign Profile is set to Don't Color Manage This Document.
step 10. I verify View > Proof Colors is off.
Can anyone provide a set of Illustrator CS6 settings that let me save a PNG image with the same colors it's drawn in so I can use that PNG image in a website?
I must be missing something obvious, because anyone working in web design must do this day in and day out, please let me know what procedure people follow to achieve this.
UPDATE:
Using the above procedure DOES preserve the colors when embedding the PNG image in a webpage viewed in Firefox and Chome, but NOT for Safari. Also, the colors are not preserved in Mac's Preview software, as well as Microsoft Office 2011 for Mac.
I'm pretty new to all this. Hoping someone can provide some perspective on what typical procedure people use for web development when working with colors in Illustrator CS6.

Answer 1

Using Illustrator CS6 on Mac OSX 10.9.1:
step 1. I open a new file for Web profile.
step 2. I verify that File > Document Color Mode is RGB.
step 3. I draw a square and set it's color to 0,103,197 (decimal).
step 4. I click File > Save For Web
step 5. In the popup that opens, I set to PNG-24, and verify the option Convert To sRGB is not selected.
step 6. Using the Mac's DigitalColorMeter, I observe the color is 0,109,191 in the Save For Web popup. If I save it, then open the saved PNG file, it's color is also 0,109,191.
How to do this so the colors don't change?
step 7. I close Save For Web popup.
step 8. I verify Edit > Color Settings for Working Spaces is set to Monitor RGB, and that the Color Management Policies for RGB is off.
step 9. I verify Edit > Assign Profile is set to Don't Color Manage This Document.
step 10. I verify View > Proof Colors is off.
Can anyone provide a set of Illustrator CS6 settings that let me save a PNG image with the same colors it's drawn in so I can use that PNG image in a website?
I must be missing something obvious, because anyone working in web design must do this day in and day out, please let me know what procedure people follow to achieve this.
UPDATE:
Using the above procedure DOES preserve the colors when embedding the PNG image in a webpage viewed in Firefox and Chome, but NOT for Safari. Also, the colors are not preserved in Mac's Preview software, as well as Microsoft Office 2011 for Mac.
I'm pretty new to all this. Hoping someone can provide some perspective on what typical procedure people use for web development when working with colors in Illustrator CS6.