That is true, however it is not why the/a stock market is irrational.
Well, first off, one person asked, the other told, but in your sentiment:
What you refer to is more likely a skew of information, a mix of information traders and (e.g.) value traders, or (generalizing term) noise traders.
There may not be a facit as to "Is this good or bad for the value of AAPL to have dividends paid out in this amount?". There may be different interpretations. Some might feel it's a sign of a new path in dividends payout from Apple even in the future. Some might think it's a short term "stunt" to keep the investors happy. Some might think it makes them less valuable as they have less money, some might think a strategy of catering to profit and investors will outweigh the "loss" in dividend payout.
Just looking at this thread of comments shows there are many interpretations.
