Hi AlexK and thanks for the interesting question.
To be honest, I never knew that InfoPath did this. It seems a bit silly, but it's probably not totally harebrained. InfoPath just doesn't know whether you are using 0/1 or false/true so it provides both. Certainly, I would think you can delete the 0/1 and just use the false/true. But, depends on the logic in your form. The 0/1 values may be useful if you are running calculations like Sum, etc.
If you aren't don't calcs, just delete the 0/1 and go with false/true.