For example, if I wanted to change the green pepper to red, could I do that?
For that specific brush you can't.
Image brushes(*) are of two kinds: color or grayscale. The color ones are replicated verbatim, and so enforce their own colors. The grayscale brushes(**) work like (inverted) opacity masks for the foreground color, the black indicating full opacity and the white full transparency.
What you can do is edit the brush image, change the colors, Select>All and Edit>Copy, and then use the 'Clipboard' brush.
(*) let's forget about parametric brushes for a while
(**) true grayscale: image is in grayscale mode when saved as a brush