Does it have to use Node.js on the server can the client side framework work with any server side JSON service?
It is very possible to use other client side frameworks such as Angular or Polymer, rather than just using Meteor's Blaze UI engine. However I find that Blaze's Template<--Helper<--Data<--Event system is extremely easy to understand and reason about.
Edit: Actually, they do seem to have a decoupled version of the Blaze UI that you could use just for your reactive DOM code and hook into a REST API. You just won't get any of the server-dependent features like full-stack automated data synchronization, hot-reload, live CSS injection, or Meteor's build chain. You just get a simple reactive template/helper/events system. http://meteor.github.io/blaze/
Meteor spans both the front-end and back-end to offer a seamless API experience when building your application.