[Paul Harrison] "Obviously I am fairly new at this, but something the editor said confuses me...she contended that the footage was by definition 'interlaced' because it was 720p 30fps..."
Your editor is confused. 720p HD is progressive at any frame rate - there are no interlaced 720-line HD formats. Cameras that shoot 24p over 60p insert duplicate frames to create a 3:2 pulldown pattern.
http://en.wikipedia.org/wiki/720p
1080-line HD is another story. 1080i/30 is akin to NTSC - 60 interlaced fields @ 29.97fps.
If you convert 720p/30 to 720p/24, your footage will appear to be slowed down to 80%.
If your editor or agent wants a 720p/24 product with normal motion (not slow motion), footage must be shot as 720p/24 to begin with. If your camera shoots 24p over 60p, then you'll need to remove the pulldown on capture. Using the 720p 24 Easy Setup in Final Cut Pro enables Advanced Pulldown removal by default.
If your camera doesn't have an option to shoot 24p Advanced (24pA), you can still confirm the 24p over 60p footage to true 24p using Cinema Tools.