The usual shape of stones helps to remove them from the goban, without disturbing other stones. Therefore, if the stone have a flat face, this face should not repose on the table.
I thought the flat side is meant to give more stability to the stones?
Rui Naiwei, 9p, asking her opponent “Why on earth all our stones are wrong side up?!”:
Well, I don’t know how those yunzi stones should be placed… I use my set mostly for reviewing games and I place mainline stones flat side down, while variations go flat side up, so they are easily removed.
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This is why I use convex stones, their 2 faces are miai 
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Obviously, you place your yunzi stones flat side down, so as to make it harder for your opponent to capture them. 
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