That didn't sound right to me, and so I checked it as follows:
Estimate for a standard classroom globe at 13" in diameter (I'm seeing a rnage of 12-14 inches as typical). I'm reporting in inches because that is what came up first and most of the globes are for sale in the US. Mixing units here, but, it works out.
But, in meters, the diameter of the Earth is 12,742,000 m on average. if we use the 'Karman line' as defining the edge of what the atmosphere is, that is 100,000 meters. Solving for X ... (13" / 12742000 m)=(X / 100,000 m). gives us an atmosphere thickness of approximately 0.1". -----
Paper glued to the globe would have a thickness of maybe, 0.004" (thin paper) to 0.012" (like a card stock paper).... so that analogy is off by an order of magnitude or more.
Even if you use the mesosphere as the definition for the top of the atmosphere, that is still 85,000 meters and thus similar.
People can check the numbers I used.
* Perhaps the analogy should go more like: the thickness of the cardboard sphere the globe is made out of is about the thickness of the atmosphere. Because, having completely destroyed a globe once in my youth, I remember the cardboard shell being approximately a tenth of an inch thick. But, that's maybe not a great reference for the analogy because not everyone has cut apart a classroom globe....