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Two thoughts...
1. This reminds me of an older thread about what holds up a car or bicycle. Consider the spokes of a bicycle wheel: they are all in tension. It is the difference between the tension in the upper and lower spokes that balances the weight of the bike. Similarly, it is the difference in pressure on the upper and lower surfaces that produces the buoyancy force. Same for the upward force that you apply with a suction cup. After all, the inside of the cup does not have to be a complete vacuum for the cup to work. But if there is air inside the cup, it exerts downward pressure. But less downward pressure than the upward pressure coming from the atmosphere.
2. The argument that "if you cut off the piling it floats so it must be in tension" had me convinced for a while. Or the reverse argument that if you wanted to add another layer to your piling, you would need glue. But you wouldn't need glue -- you would just need to have smooth enough surfaces to push out all the water (which brings us back to the question that started the thread). It is not a realistic way to make a piling, but it does show that without any upward component to the water pressure, the piling is in fact in compression. Cutting part of it off introduces another surface for water pressure to act on.