If that is true, then it’s really bad news. No search solution can access data from outside WordPress, there has to be some sort of an abstraction in the local database so WordPress can return something. Usually the item titles and metadata is stored in a post type to make them searchable, and then search plugins can at least search and return that, even if the file is on a remote location.
If there is no post type associated with each file in the local database, then I’m afraid there is no search plugin that is able to search these, as they all rely on the local post type mapping.
You should ask this to confirm, just to be sure that there is nothing stored locally in a post type. If not then probably the simplest and easiest solution is to somehow custom code this to the other plugin so that the remote file metadata (title, date, download url etc..) is sinced to a local post type so it can be used for search purposes.