You might want to suggest to your friend that 'applique' is an umbrella term under which there are several types of methods. She knows that there are other methods of applique than the one that she likes to use, such as hand whip stitched, or machine zig zagged. The method of applique your friend is doing is 'needle turn applique.' Your method is 'fusible raw edge applique.' I've also seen plenty of raw edge applique that doesn't employ any fusible interface.
Here is another example: people use 1/8" satin ribbon, or yarn, or cotton floss to stitch flowers, and call all of the methods embroidery.
Someone could say about one of my pieced quilts that it's a 'collage of color.' I would agree; my quilts are a collage of color-- but that doesn't necessarily mean that my quilts are collages. The argument you have seems to be just a disagreement about semantics. English is a language with a plethora of descriptive words!