Well, you're wrong about one thing: that's not just small businesses in Turkey. Even very large chain stores have the same level of hospitality. And it's not just stores. As an example, tomorrow is the start of Şeker Bayramı (literally translates as "Sugar Holiday" but is just what Turks call Eid al-Fitr, the end of Ramadan). The holiday lasts for 3 days. I received a text from Turkcell the other day stating that they were giving everyone unlimited texting during the holiday.

Edit: Also, of course the Turkish businessman is making back the cost of the tea. It would be foolish to think otherwise. The point is that (if you want to go all Econ 101 on it...) Turks tend to think in terms of straight profit, whereas Americans are much more obsessed with opportunity cost.