The border fabric is very important and can make or not make a quilt just right. The border is like the picture frame. It pulls all the colors together from the quilt and gives the eye a place to rest...especially when a 1 fabric border. Pieced borders are harder to do, but are good for using lots of the colors from the center of the quilt and in that way they pull the quilt together. If I do a pieced border, I like to do an inner border first.
A lot of times I pick out the border fabric first...and then pull colors from that fabric to choose the colors for the quilt. That way I have a fabric that I know is going to work well for the border.
The border for that quilt must have been chosen for a reason, but if the reason was it was "in the stash", that wouldn't be the best reason to use it if it doesn't do anything for the quilt...better then to go shopping!