Paper money is merely a placeholder for value. It has no value itself, even though we associate value with it. No billionaire would ever want to convert very much of his/her value at any one time to paper currency because that is the least useful place to put it. And think about the process by which this would happen if it did. The billionaire would have to sell his assets (his factory, his farm, his oil well) to someone else for an agreed upon price. The price is set exactly as described in the Apple example above, based on the buyer's faith in the asset's future.
In the real world, though, the only rational reason for converting value to paper money is as a means to exchange the value for goods or services. Only a small percentage of the value in the economy is represented by actual paper dollars. When an investor talks about buying dollars what they really mean is putting their money into bank-like investments where they earn interest for allowing others to use their money.
So, no, currency does not need to be printed in order for value to be created. Currency is simply a method for exchanging value. As far as the amount necessary, there just has to be enough that when I want to convert my value in a liquid asset to currency that I can immediately do it. If I go down to the bank and ask to convert my account to actual cash, and they say, "Sorry, we're out," then all hell breaks loose. And the reason it breaks loose is not because the value of paper dollars has changed at all (they are essentially worthless and always will be). It is because my faith in the dollar has changed.