...I never fly out

Hit 'em hard and straight, eh? Trés bon!

I thought your explanation was very good, me.
I think "flied out" is caused by the same type of mentality
that made you-all call your $2 money 'two-ny', after loony.
I guess the absolutely correct phrase is: (the batter)
hit a fly ball (which was caught, thus earning the team an out). But to say the batter "hit out" would be much too confusing (hit out of the field completely? hit out of the
fair area?). Fly-balled, or flied, out, tells exactly what
happened.