the "controller" in MVC is specifically tasked with responding to user input and persisting those changes into the model. So it's nothing like a database view either, which is traditionally read-only. Like a database view, a template organizes information from disparate sources into a particular presentational configuration - just at different levels of the stack. IMHO they are roughly analogous.
Wikipedia credits Trygve Reenskaug with inventing the term "model-view-controller", he was a Smalltalk guy with Xerox at that time - I don't think there's any relation in the origin of that terminology to the notion of a "database view" - otherwise not sure what you're referring to here (here's a link to the original paper: http://st-www.cs.illinois.edu/users/smarch/st-docs/mvc.html)