That cannot be true about that paper, because it uses an expansion in a "small parameter" relating to the mass ratio. If the mass ratio is unity, their approach does not achieve its objective.
Yes, indistinguishability would be an interesting wrinkle to an exercise like that, it would interesting if it mattered in some way as to how that "cut" comes about!
If they are looking for a mathematical answer, then yes, that would be a good way to go. If they are looking for a physical description of what is going on, or if they don't have that text handy, then other kinds of answers could be useful, perhaps along the lines of those given above.