The purpose of the simple songs like Jingle Bells is to get your hands used to moving the way they should. Like you said, you need to start small first. People who make lessons use those easy bits because they know everyone knows them and they are simple to start with. You could technically just play any random notes, but familiar songs make it at least a little more interesting.

Once you are comfortable holding the pick, hitting/fretting notes, strumming chords, and all that basic stuff, feel free to branch out of the extremely simple stuff. That's all they are trying to teach you.

By the way, since I can't view that lesson, what is it teaching you. Standard notation, tabs, or something else?