Update the actual file associated with a file entity while keeping the fid? Media module provides a generic.png file that it copies into /sites/default/media-icons/generic. That file is used on my site ~300 times, but I'd like to replace it with another PNG. Is it possible to replace the actual file that is associated with that file entity? Ideally I'd keep the generic.png name, but I can use an updated file name if needed.

I've tried simply replacing the file in /sites/default but that had no effect.
As @clive noted in the comments, all that is needed is to replace the file itself. We were having some other server issues that were causing the change not to show up. You may need to flush your image styles in order for those to pick up the new image, though.