Friction - settling a question

Talking about friction, we rubbed our hands across the desk and the carpet. "Which is easier?" asked Mr Gregg. We couldn't agree: some thought the desk, some thought the carpet.

So... a scientific experiment. Measure the force it takes to move a stone in a bag on the two surfaces. Which would take more force?

The carpet took more force: 10 Newtons, compared to just 5 on the desk. There must be more friction on the carpet.

But Tibo said, "It's not fair. The bag makes it easier on the desk."

Half the class agreed. So we untied the bag, and tried the stone directly on the two surfaces:

This time it took 10 Newtons on the carpet, and only 2 Newtons on the desk. There's definitely more friction on the carpet!

Now the only question is, why didn't we agree that in the beginning?