Using "on" for flat things and "on top of" for tall things is not a hard and fast rule. It may be attempting to provide a starting point for people new to English, but it does not apply in all cases. You could say "the loudspeaker is on the speaker stand" even though the speaker stand is very tall and thin. Also "The book is on the stool".
Lindstromberg writes (page 231) in his advice on teaching prepositions: "Demonstrate or draw, for example, 'on the paper' and 'on top of the bottle'. Show that we can also say 'on the bottle', but add that on top of is what we often say for tall things.". The key word is "often". Native speakers do often say that, but it is a not a rule, and not what exclusively determines the use of "on top of". Lindstromberg is not trying to explain definitively the use prepositions, he is writing about how to effectively teach the general use of prepositions.
A better way to think about this is that "on top of" is used mainly where "on" might have an unclear meaning. With the case of the paper, "on the paper" might well mean "drawn on the paper", so if there is any danger of confusion you say "on top of". But if someone asks "where did I leave my pen" you can say "your pen is on the paper" without any danger of confusion, so you do.
Likewise "the label is on the bottle" generally means it is attached to the bottle on its flat vertical side. If the label is really resting on the top of the bottle, you would use "on top of" to avoid confusion. This is probably where your author gets his rule from. Many tall thin things can have objects "on" their sides (like a label on a bottle), so if you want to make it clear that the label is sitting on the top of the bottle you would say "on top of".
To answer your specific question, it is grammatically correct to say "the pen is on top of the paper", but most English speakers would not use it unless there was a possibility of being misunderstood. If you were referring to a picture resting on the paper you might say "the picture is on top of the paper" to distinguish from the case where the picture might be drawn on the paper. If the pen was right at the top of a big pile of paper you might say "the pen is on top of the paper" to distinguish it from the case where the pen is on some other part of the pile.
TLDR: Use "on top of" when "on" might be misunderstood. Or possibly for emphasis.