Yes, as far as I know anyway. All the Colour option does is to over lay a colour over the top of the texture with different amounts of transparency, so the base colour will always show through to some degree.
Your best bet is to open the texture file in Photoshop (other Graphics programs are available) & edit & save the texture twice, removing the colour saturation & creating the greyscales you want. You can copy & paste the link shown below in Windows Explorer to get the file location.
Agree with Kevin Pymm. Edit the image, and then point the image path to the altered image. I would at that point be inclined to click the 'Save Appearance' button up the dialog. I wouldn't save it in the default SW location as you run the risk of losing it at the next install. Obviously, you can do this with images you take yourself or source (legally *cough*) off the internet.
This texture stuff always trips me up!
Doing as you have said I can now change the colour of the burlap.jpg and save as a light grey.jpg and a dark grey.jpg.
This was obviously done through graphics software like you said and both of the new colour .jpgs are saved in the same folder as where the original .jpg is.
Where I have trouble, and always seem to, is now creating the p2m file with those colours..........
**** EDIT ****
Thanks very much Kevin
in the illumination tab, look at turning down the reflection.
Also worth a play around is the specularity settings.