On the 737 you usually use the autopilot/flight director system of the pilot flying. In this case this was the first officer in training and therefore it was normal procedure to use autopilot B.
So far i have not seen any indication if the crew was aware of the RA problems on RA1 or not.
And please guys, try at least to read the available information. The "faulty" (more correct: erronous reading) instrument in question was the RA which has nothing to do with the pitot-static system.