Actually, one of the sources you just linked (Wikibooks) states that officers were usually promoted from the ranks:

They were generally moved up from the ranks, but in some cases could be direct appointments from the Emperor or other higher ranking officials.

For further sources saying the same thing, see here, here, here, or here. See also this:

The most significant step in any successful army career of a Roman plebeian was the promotion to the centurionate. To become a centurion meant having become an officer. The main supply for the centurionate of the legions did indeed come from the ordinary men from the ranks of the legion. Though there was a significant number of centurions from the equestrian rank. Some of the late emperors of the empire prove very rare examples of ordinary soldiers who rose all the way through the ranks to become high-ranking commanders. But in general the rank of primus pilus, the most senior centurion in a legion, was as high as a ordinary man could reach.