News stories are freely available information, published for public use. However, try copying the Washington Post onto your own webserver and allowing free access to it, and see how legal that turns out to be.
While their website is ambiguous (I don't see a "terms of use" page anywhere), I seriously doubt that airnav.com would take kindly to AdventurePilot crawling their site to mine fuel pricing data wihtout any compensation. AirNav makes money by selling ads on its website. People will only buy ads if folks are visiting the website. One way Airnav gets people to visit is via the AirBoss program, which encourages operators to use the Airnav.com site to check for fuel prices. FBOs have agreements with airnav.com to communicate their fuel prices to airnav and to honor the prices posted there.
That is effort that airnav.com is expending to gather fuel pricing data, and it's a part of their business model.
To go pilfer that data for your own business could be considered stealing.
As far as I know, there is no "free, publicly available" database of avgas fuel prices. The FAA doesn't collect that data and make it freely availalbe. Anyone else who collects it is expending effort to do so and creating a product that has value, and they deserve to be compensated for it.