The app is the most accurate. Does your phone by chance have a "battery saving" mode? If so, try turning that function off. It helps immensely with my phone and the Disney apps. I always have to turn off my battery saver and no more app crashes.
Disney most likely doesn't give any 3rd party access to 'real time' wait information, if such a thing actually exists. They would need some kind of line sensors on every ride to do that.
In my experiences, the Touring Plan app is very accurate. It also doesn't go down all the time like Disney's, which is very important!
Overall, I find the $15 that I pay for the Touring Plan subscription to be well worth the money between the app with the wait times, the crowd calendars, the personalized touring plans I create and the APR finding. Just my two cents!