Correct Way to Integrate Material UI with Meteor 1.3 beta/React?

Yes. You need to do this in your topmost container:

import React from 'react'
import MuiThemeProvider from 'material-ui/styles/MuiThemeProvider'
import getMuiTheme from 'material-ui/styles/getMuiTheme'
import lightBaseTheme from 'material-ui/styles/baseThemes/lightBaseTheme'

const lightMuiTheme = getMuiTheme(lightBaseTheme);

const App = React.createClass({
    render(){
        return(
            <MuiThemeProvider muiTheme={lightMuiTheme}>
                <div>
                    [... rest goes here...]
                </div>
            </MuiThemeProvider>
        )
    }
});

They changed that a bit when going from v14 to v15. For some reason, they also insist on not providing infos about breaking changes on their documentation. For that, you have to search the GitHub repo and go through the release notes.

Also, when going through said documentation, make sure that you’re selecting v15-beta.2 in the dropdown as that’s the version you’re likely on if you’re using React@v15