I think asking for explicit permission from the original author is best. I think you should at least offer to provide the story, prepublication. Opening up communication with the original author has added benefits. You may gain more insight into the original story. The conversation itself may be enjoyable.
You need to preserve the "integrity" of the original story. Readers should consider the original "complete" and capable of standing on its own. There are exceptions. For instance when you are "World building".
The " Finding Forrester" technique is not as different as it sounds. It may even be common. (I'm always tempted to change that into "The Finding Forrest Gump Technique".
kdpierre:
This is an interesting concept, and the responses are equally intriguing. Personally, I can't imagine ever doing it, nor can I imagine anyone using a story of mine for this purpose,
In this case kd, your imagination is much too limited. Maybe you, or other wonderful authors, like Bashfulbob, would be more comfortable considering yourselves as "influences". Stories can become " models". I don't know exactly when plagiarism becomes an issue.
I also think of a story and as the author's "baby". I would never change the original.