Actually the installation link is something that we create on the fly after upload. The public link is the link to the public HockeyApp page (i.e. the non management page) that allows your team to download all available versions. HockeyApp doesn't appear to provide the direct installation link in the upload response. So we still need to create the installation link ourselves.
However, you're correct in that if you have upload only API key on HockeyApp then we shouldn't be creating an installation link as it makes no sense under those circumstances since we are not allowed to create releases on HockeyApp in those circumstances.