I had never heard this version of the myth before. The "myth" I have heard, is that if you do a search on say Travelocity for example and then go and search Expedia or another site, you will see lower prices. This myth, to me at least, is a little more plausible, although in my own comparison I have never seen a major difference in prices to get me to convert from one site to the other. Obviously each of these sites competes against one another for bookings and traffic, so if they know you are "shopping around", by checking if a cookie exists from another site, it is in their best interest to offer lower prices.
@jeffmould What you describe is absolutely true and no myth at all. There are several reasons for that.
1. Price differences may occur because all Online Travel Agencies (OTA) mostly provide cached data to the user as requesting live prices can be super expensive. Differences in the age of the cache cause the difference
2. Some OTAs have so called negotiated fares with the airlines and sometimes can offer different prices
But, when we as metasearch request prices from the OTAs, we always do that from the same IP with cookies
Summary: No. "Flight prices are most likely impacted by three factors: complexity of airfare pricing, high demand for the same flight and cached data."