I think you're confusing the two meanings of "free". See http://en.wikipedia.org/wiki/Gratis_versus_Libre. RMS is likely advocating for free as in free of restrictions, not per se "at zero cost".
Sure, and there is the possibility of free-as-in-freedom libre software-as-a-service. And web APIs that are free software. The OpenStreetMap API, for instance. The software that runs it is open source, the data is freely licensed, the system that it runs on is open source (Ubuntu Linux, Apache, Ruby on Rails)...
no, I mean free in the libre sense.
There are plenty of free SaaS providers out there, basically anybody who provides git hosting, apache/php hosting, wordpress hosting or email hosting (using a free stack) is doing this.