Piwigo is meant to publish photos, there is no encryption and there's always the possibility that even for private albums single URIs to individual pictures are passed on. Anyhow, whoever has access rights can copy-paste URIs, but of course can also copy-paste images. So either you trust them or you don't, and your hosting provider has access anyway.

But there's a simple solution to the access right problem and URIs handed out to not authenticated/authorised persons, setup a gallery in a directory with an Apache .htaccess .htpasswd secured authentication. Which doesn't change anything about trust though.

Besides, the general rule that if you want to keep something strictly private then don't put it on the internet of course applies.

Regarding Piwigo "employees", unless you have your site hosted by piwigo.com there's no "employee" involved with your site. ("employee" in quotes because it's only 'plg' who has last say about Piwigo's code).