Is it illegal to link to a copyrighted file, even if it was uploaded by the owner (with an publicly accessible URL (with a password in it) but with no intention to make file downloadable by anyone)?
It is hard to say: this article sketches the legal landscape. So-called deep linking that bypasses the main page for a site is not believed to be infringement, following the reasoning of Perfect 10, Inc. v. Amazon.com, Inc., 508 F.3d 1146. The URL itself does not have the bare minimum of creativity required for copyright protection, and storing a URL on a computer is not storing the contents that it refers to, so no copy was made in violation of copyright law. It is unlikely that competing theories would develop in other US districts (there don't appear to be any at the present).
However, such a link could create secondary liability for infringement, see Erickson Productions, Inc. v. Kast, where a party "has knowledge of another’s infringement and (2) either (a) materially contributes to or (b) induces that infringement". If I link to a file on a pirate website, I am secondarily liable for that infringement. However, if I link to a legally-uploaded file which the author did not intend to make public, there is no infringement.
Copyright law requires permission of the copyright owner, which is more than just "explicit denial". The problem is that a person can put a file out there and not say one way or the other whether you have permission to copy the file. The US Copyright office says that "A copyright owner must have expressly or implicitly authorized users to make retainable copies of a work by downloading, printing, or other means for the work to be considered published" (let's not care at the moment whether it is important to be "published"). The court may infer implicit permission from a copyright owner's conduct, but there is no rule "if it's on the internet, you've granted permission". A rights-owner may make a valiant but insufficient effort to block access to the work (except via a password), so in that context, the courts would infer that the rights-owner had not given permission, therefore the copying is infringing and you have secondary liability for your direct link to the material.