I trust Peter more often than myself, but, I believe this is a case of simply toggling the Update Graphic Links in Package.
I have placed a link which is local and available to my machine, toggled the Update option, and in this Packaged Document ID is linking to a mapped location where I saved the folder.
I believe the setting is sticky.
I think there's a subtle difference between what you and the OP have done.
You saved the folder to an new location ans updated the links in the packaged file, so they now point to the package folder. If you do as the OP says and "copy and paste" to a new location and leave the original behind, I think you'll find the links are still pointing to the same folder where you originally saved the package, not to the pasted location.
If you CUT and paste, or otherwise remove the files from the locations where they were originally saved, ID will find them in the new location.
I see the issue frequently with packages (it is a pet peeve) and believe the answer is, as stated, to toggle the Update Links in Packaged Folder option.
I have moved (cut from original location) the test folder as the OP does and ID links to the package folder. The original location is still available, but ID, to my testing, respects the packaged link...
test - delete the package link to check if ID will look to the first, original, in-tact location...
In this instance, ID does not look to the original location. All my testing confirms that once Update Links in Package is choosen, ID no longer looks to the original location.
As I stated, I belive the Update Option is sticky, needs to be set only once upon which the option is the new default. I think it would be a better choice for "out of the box" installation, but I am not feeling it need to submit a Feature Request.
OK, I don't think you quite grasped what I was saying, or I'm completley wrong about ID.
In your ID file you place an image tha is linked to Location A. That's a hard link.
You package the file, and save to Location B, and in the Package dialog you click the Update Links in Package box. The links, in the packaged copy of the file (and only that copy) are now pointing to the links folder in Location B. These are also hard links. The original file is till in Location A, but the packaged copy doesn't care about that because it has links to Location B. So far, so good, and I think we're all on the same page up to this point.
NOW, you make a copy of the packaged folder and put it in Location C. The copy of the .indd file inside the copy of the package in Location C still has links to Location B. IF the original package folder is also left in Location B, the Location C copy of the .indd is going to use the link in Location B, not the link in Location C. The only time the links in Location C will be used is if Location B is no longer acessible.
Was that any clearer? Am I still trustworthy?