The license to access private property is based on the intent of the property owner. Where the intent is made express (through a sign), that governs. Where the intent is not made express, we try to figure out what a reasonable person would infer about the property owner's intent.
The method of access, therefore, is relevant insofar as it tells you about what the owner of the web server intended people to have access to. The fact that content on a website meant for the public to access is only accessible by "programmatic" means that ordinary users would not know, is strong evidence that the owners of the web server did not intend for people to access those documents.