I think CW has it right. All this duplication is bad, and to really get a satisfactory solution a redesign from the ground up is needed.
In the long run, I think AGS should move to having the source files as part of the project, so they can be updated simply by updating the file (how to deal with animated gifs, tiled sprites, and transparency settings is a bit of an open question, as is the question of how resource indexing would work if a file goes missing), which would also improve source control support. AGS should also use the file system folder structure to organize sprites, scripts, audio files, etc., rather than forcing users to duplicate this organization themselves. All file references should be internal to the project, and relative to the root folder path, so that a project could be shared without breaking any references.
In the short run, I think adding another configuration setting so that everyone gets to have it however they like is not a good idea. One definition of design is to impose constraints on a problem, or in other words, to make decisions. But since Pumaman, CW and the other AGS developers have always been bombarded with different opinions and ideas, all too often the "decision" has been to have it both ways: to make it optional, configurable. In the long run, all these configuration options makes the system hard to learn and understand, difficult to support and debug (if someone has a problem, you first need to figure out exactly which of a million possible configurations they're using), and increasingly impossible to maintain.
So if we need a short-term solution before moving on to a (possible) future redesign, I would urge the devs to just consider the different arguments carefully, and then making a decision, not try to cover every individual preference as a separate setting. In this case, I think the simplest solution would be to store the relative path if the file is within the project folder (or a subfolder), and the absolute path otherwise. Users can address the other use-cases RickJ brings up by linking sub-folders of the project to a repository however they want; AGS shouldn't have to be involved in that. But that's just my opinion.