Bonjour wurp,
I went on the site but never found the tutorial itself. Could you provide us a link more specific than just www.dvgarage.com ?
Now how to map the grime. You're right, you can do exactly what you want with a mix2color node. But first you'll have to put an alpha channel into the grime image file, in Photoshop. I'm sure you already know that, the alpha channel defines the visibility of the rgb channels. Black means transparency, white means opacity.
So here is how to use this in XSI. Open the Render Tree, and connect your Image node, that is connected into the color1 input, into the weight1 input. Then you can play with the Mode settings, try checking the Multiply by Alpha option.

There is 2 other ways of doing this.
1-You can achieve different results than simply plugging directly your Image node into the weight1 input. Try this: load a Pick_Channel node (Node > Channels > Picker), and plug the Image node into its input. Open the Picker node, and set the Channel to Alpha. Then, load a Scalar2color, and plug it into the weight1 input. Finally, plug the Pick_Channel into the Scalar2color.

2-Instead of connecting the same Image node into the color1 and weight1 inputs, create a new Image node (Node > Texture > Image) and connect it into the weight1 input. The image you'll place in this new Image node is the alpha channel you created earlier. Take this alpha channel, copy it, paste it into a new file, save it, and this is the image you'll use as the weight.

Hope this helps
Salutations - Cheers
Bernard Lebel