It works. I do it all the time.
look on page 109 of your manual for info on connecting to a computer. This should fix your problem. Since you didn’t mention what format you recoded its harder to answer.
IN MENU
HDV= video output set {PLAYBACK STD} to {HDV} and {HD DOWN-CONV} TO {OFF}
IN FINAL CUT USE HDV EASY SETUP WITH HDV FIREWIRE BASIC.
Good Luck