A guitar built "right handed" would need more changing than simply turning it upside down and stringing it "backwards".
The nut will be cut to have the strings in the usual slots for right-handed playing and so would need swapping for a left-handed one (the thinnest slot in the nut would be where the heaviest string is if you turn the guitar over). The bridge and saddle would alse need some alteration - the intonation slope on the saddle would be in the wrong direction, and if the saddle is cut to give the highest action on the would strings that would need reversing as well.
For left-handed acoustic playing on a relatively inexpensive instrument it's easier to get a left-handed guitar, because having the necessary alterations done to a right-hander could add quite a bit to the cost. Unfortunately "cheap", "good" and "left handed acoustic guitar" are words not often found together.
It's generally much easier to "left" a "right" electric guitar but a new nut (at least) is still required and the ergonomics might not be ideal (not that Hendrix seemed to have a problem).
Another option is to play the guitar right-handed - there are some very good guitarists around who do this. Finally there's the Dick Dale option - just turn the guitar over and play with the strings reversed from where they're "supposed" to be.