Riddle

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Just grab the bill. You didn't say it was under the tip.

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Also, I've heard this riddle before and there isn't an answer. You worded it wrong. Removing the bill intact, given the parameters

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In high-school level classical mechanics, yes, you are told the maximum magnitude of static friction is simply a coefficient µs (depending on the materials) times the magnitude of the normal force, FN. This is independent of area because the smaller the area, the greater the contact pressure and so the more interlocked the uneven surfaces become, meaning more static friction per unit area. Thus sliding the inverted pyramid will not be feasible in this model.

In reality this nice area-independence would probably break down for such high pressure. Coefficients of static friction are recognized as cute toy models suitable for high school but they are not terribly accurate in the real world. In physics language, you have moved beyond the linear regime.

More interesting is the idea of tipping the pyramid over. It may be perfectly balanced, yes, but it is in unstable equilibrium. That is, classically, even the smallest perturbation to the system will grow in a positive feedback loop. Unless your model specifies that there is a static friction torque at the apex, a slight push will angle the pyramid slighty, and then gravity will take the whole thing down for you. This is true no matter how much inertia the object has (even though it may not seem like it - you have to mentally separate notions of "arbitrarily small effect" and "zero effect").

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