Package installed from private repository is being listed as being installed from public repository

Brief description of your issue

When installing an application from our internal WinGet repository, WinGet is listing the package as being installed from the public WinGet repository.

Steps to reproduce

Upload a package to an internal WinGet repository, where the same package exists in the public WinGet repository.
Install the package from the private repository.
Export the list of installed packages. It will show the package as being installed from the public repository, not the private one.

Expected behavior

I would expect WinGet to show the package as being installed from the correct repository.

Actual behavior

WinGet shows the package as being installed from the wrong repository.

Environment

Windows Package Manager v1.6.3482
Copyright (c) Microsoft Corporation. All rights reserved.

Windows: Windows.Desktop v10.0.19045.3803
System Architecture: X64
Package: Microsoft.DesktopAppInstaller v1.21.3482.0

Start by reproducing the private-repository installation and package export described in the issue, then trace how the REST source records repository provenance. Done means an export identifies the private repository when the package was installed from it, rather than the matching public repository.