This statement may have been true before the rise of low-cost carriers, and indeed, in the 2000s I occasionally caught cheap fifth-freedom fares like SIN-HKG on United or KUL-CGK on KLM that were cheaper than the big boys (SQ/CX and MH/GA respectively).
These days, though, low-cost carriers that cut costs to the bone and make up for it with ancillaries (checked bags, meals, seat selection etc) can offer much lower no-frills fares when booked in advance: Air Asia, Lion etc are now by far the cheapest options for KUL-CGK, while Scoot and HK Express rule SIN-HKG. Fifth-freedom carriers can't really compete in price alone, and with new planes making longer point-to-point flights feasible many of these old segments have been dropped.
Edit: I know Skeptics.SE likes references, but historical fare data is kept under lock and key and flight schedules & pricing are currently messed up by COVID. The overall ascent of LCCs and decline of fifth freedom flights is well known though, see eg this article from industry analyst Sam Chui:
Until 2017, United Airlines operated several fifth freedom flights from the United States to cities like Hong Kong and Singapore via their Tokyo-Narita hub.
However, a new generation of twin-engine, fuel efficient and long-range aircraft, like the Boeing 787 and Airbus A350, have made such intra-Asia flights obsolete. In 2017, United Airlines began a nonstop service between San Francisco and Singapore on their 787-9 aircraft. Doing so, ended their historic fifth freedom service between Hong Kong and Singapore.
https://samchui.com/2020/09/15/aviation-analysis-revival-of-fifth-freedom-flights/