OS X Color matching on dual displays

I have an iMac and a second display - an LG 24" panel.

Using any colour picker (eg Digital Color Meter) on exactly the same colour gives a different result depending on which screen I pick the colour from.

As an example - on a web page, the body colour is defined as #c00202.

On the iMac's display, the colour picker gives me the expected value of #c00202, but on my other display, I get a different value - in this case #bc0007. If I change the display profile. I get a different value.

I get what's going on, but is there any way of just making the colour picker return the defined colour - it seems crazy that I'll get a different value depending on which screen I'm using.

When selecting "Display native values", the actual value depends on the color profile of the monitor, which explains the difference.

Forcing a single profile, like sRGB, should give the same result across different screens.