This is probably accurate for films and fabrics, but I wouldn't be surprised if thick solids would be at least as slow to rot as wood. I don't know what proportion of plastic mass is in each form though.
Wood is a nice analogy because when it was first evolved there was nothing on earth that could break down the lignin. As a result, we had a couple thousand years where wood just piled up like a global waste crisis. Eventually fungi got really good at dealing with it
We're again seeing a waste crisis due to a novel material and once again fungi might end up saving us (though we don't have a thousand years to wait this time)
What makes you believe "rot like paper" is more appropriate than "rot like wood"?