I believe it is more of how they have coded the site for authentication of a user over the search engine.
You can do an If/Else statement within the PHP code. My example is as follows, and I will be using GoogleBot as an example for this.
$googleBot = $_SERVER['HTTP_USER_AGENT']; // Defines it as GoogleBot Instead
// Allows indexing of the full site and goes over the limit of 20
// Everyone else is only allowed to view the site so many times
Google does have to deal with the limit also. There may be a time-limit of how long till Google and yourself can view so many pages again. If so, Google will index pages at that limit also, but it will take a good while to achieve this indexing of the site.
I'm going to agree with closetnoc. That is not cloaking. Rules applying to "users" and "bots" are slightly different when you want Google to index your site easily, so that goes back into Answer A with how they are most likely doing it.
Also, you are seeing the same content as Google, but you are only allowed to view it so many times unlike Google.