This is also why people like Richard Stallman are clear to distinguish the
freedom concerns of SASS from the freedom concerns of programs running on
one's own computer.
Stallman's definition of SaaSS excludes search engine. See
https://www.gnu.org/philosophy/who-does-that-server-really-serve.html :
Services such as search engines collect data from around the web and let you
examine it. Looking through their collection of data isn't your own computing
in the usual sense—you didn't provide that collection—so using such a
service to search the web is not SaaSS.