That's because the company's name is AOL, Inc.[1], and not an abbreviation. It doesn't have anything to do with the pronunciation. AOL used to be known as America Online, but when it bought Time Warner, the new company was called "AOL Time Warner"[2].
The Times also writes "I.B.M." instead of IBM, because it is officially "International Business Machines". They also used to write "A.T.&T." for "American Telephone and Telegraph" [3], but now write "AT&T" when AT&T changed their name to the former acronym.
