No. By market cap, Apple is the largest company in the world, full stop[1]. Microsoft is number 7, having spent much of the 90's at #1. Google does not rank at all. So at least by some definitions these companies are indeed the largest in the world without qualification.
Market cap is one indicator. You can also look at full capitalization, ie debt plus equity. Or you look at number of employees, or total sales. Also, quoting your Wikipedia article: "Some state-owned companies are far larger than even the largest public corporation. For example Saudi Aramco's value has been estimated at $10 trillion, which is twenty times the size of Apple [...]."
Anyway, Apple and Microsoft are pretty big and dominating in their industries. No doubt about that.
[1] http://en.wikipedia.org/wiki/List_of_corporations_by_market_...