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That's not part of the pitch for Meteor. Take a look at point 6 on the Meteor homepage:

Sensitive code runs in a privileged environment: Write all of your code in JavaScript (if you want.) The user interface runs in your browser. The sensitive functions run in a privileged server environment.

You're missing that the pitch with these things is there is no server code as such.

For Firebase, yes that is part of the pitch. Personally the use case for Firebase doesn't really appeal to me. For Meteor, it's the opposite. The fact that you can write some server-only code is a plus.

That's simply untrue, at least as far as Meteor goes. One of their big selling points is, in fact, that there IS server code.