Monk was produced by Touchstone Television and was originally presented to ABC as a possible new series. But ABC was riding high with Who Wants to be a Millionaire at the time and wasn't interested in the quirky series. (It also rejected other shows such as CSI and The Sopranos for similar reasons.) When an acquisitions person at USA Network heard of the rejection, the show was brought to the attention of the network's management who were looking for an original series that would help USA stick out from the pack. They believed Monk to be just that show. And it was, well beyond everyone's wildest dreams.
So while the show wasn't airing on ABC, it was being produced by a Disney subsidiary, though the company was not making as much cash as it would have if ABC was airing it. After Who Wants to be a Millionaire imploded, the network was reduced to rubble. They had rejected a slew of programs that were now successfully airing against ABC. The network tried to make a deal they thought USA couldn't refuse; ABC would take new episodes of the show first, then let USA air them for free. An unprecedented deal, but USA didn't take it, leaving ABC with the unenviable task of rebuilding itself. (Something it would do seemingly easily with the introduction of Lost & Desperate Housewives just a few years later.)
The show would eventually go out with a bang, leaving USA Network with the highest ratings of any basic cable series in history.