That seems way too cheap for a ride that far. It wouldn't be very expensive but I doubt it would be 260 yen. Not sure if there's a better way to get how much the actual cost would be unless you are looking at a train map in a Japanese station.
i'd say you found a bug. None of those trains are free and the app is saying 0 yen.
I end up using google more than anything else, because it can also take into account walking and other alternative routes. the apps that focus on trains alone usually don't take into consideration things like walking between stations to reduce the complexity of the route.
You can see from the Monorail fare table alone that the cost for an adult is 490 to Hamamatsucho.
The limousine bus service (airport shuttle) between the two airports is here. Adult fare is 3100 yen.
Keisei train access via Access Express is 1800 yen.
Compare the travel times here. Keep in mind that on the bus, you can store bags in its compartment, so you don't have to lug them to your seat, which is a tight fit and has only small overhead space. I forget whether the Keisei train has a storage section of each car.
Looks like your phone has received invalid data. Easiest route between the two airports by train is with one transfer at Shinagawa.
Both Hyperdia and Google maps have flaws in planning and route suggestions - for most people you will not notice. The route shown in the images of the 1st post is not very good.