Directory Traversal - sanitize_filename()

[eluser]echo_boom[/eluser]
Does the danger from directory traversal come from PROCESSING an unsafe filename OR does the danger come from STORING an unsafe filename as it was originally named?

For example: if someone were to try and upload an image with an unsafe filename, and you simply renamed it, is everything ok? OR do you have to sanitize the filename BEFORE you rename it or do any kind of processing?