The value of this flight to the US Government in general and the Navy in particular was realized before she ever took off. By giving Roosevelt a domestic and internationally acceptable excuse for inhabiting Howland and building an airfield there, it strengthened the territorial claim and the validity of trans-Pacific aviation, which could provide cover for future surveillance work if necessary. Remember, we only had a few islands in the Northern Pacific at the time; the rest were held by the Japanese.
Suppose someone floated the idea of having her take a few pictures of Truk or intercept radio communications en route. You have to believe that they thought they/she could:
1. Convince her to become a spy. A civilian engaged in military espionage. Internationally recognized as a capital crime.
2. Equip the plane to bring back something worthwhile.
3. Train her and FN to use the equipment.
4. Extend and complicate a flight plan already on the ragged edge of plausability.
5. Allow the flight to proceed without a comm plan that would coordinate frequencies and schedules.
6. Execute the mission without getting caught.
7. Return to US territory safely.
8. Keep it secret.
If they wanted to try this on the first attempt, it meant also having the additional crew in on the deal; Manning and Mantz survived the flights with no later indication of any espionage involvement.
If they wanted to stick with the idea after the Luke Field performance, they only had a matter of weeks to retool the mission to go in the opposite direction.
None of the above things can be demonstrated to be impossible, therefore they are possible, but the idea that the administration would risk war with Japan by running those kinds of odds borders on ludicrous.
Find the plane and check for spy cameras or recording equipment. It shouldn't be hard to find, here was the state of the recording art less than five years before the flight (from wikipedia entry on magnetic tape.):
"On Christmas Day 1932 the British Broadcasting Corporation first used a tape recorder for their broadcasts. The device used was a Marconi-Stille recorder, a huge tape machine which used steel razor tape 3 mm wide and 0.08 mm thick. In order to reproduce the higher audio frequencies it was necessary to run the tape at 90 metres per minute past the recording and reproducing heads. This meant that the length of tape required for a half-hour programme was nearly 3 kilometres and a full reel weighed 25 kg. For safety reasons these machines would only be operated in a locked room by remote control. Due to the tape's speed, springiness and razor-like sharp edges, if the tape broke while in operation, it could unspool, fly off and cause serious injury. Besides this, the methods of recording could lead to massive data loss and poor audio quality because of their nature."
Magnetic tape was developed by BASF during the thirties, but the US didn't really get into the game until after WWII.
Of course the government had interest in the flight; they spent a bunch of money to support it. It's just asking an awful lot with very little supporting evidence to accept that she had an intelligence tasking for this flight.