A lot of consumer camcorder manufacturers have "different" ideas about how to record video. My older Samsung documentation said the same thing -- records in 60i but is supposed to produce 30p. Never really worked out well in FCP7, not to mention that the anamorphic SD footage never translated either. The way I figure it: the camera records 60 interlaced frames per second, but is reformatted with every 2 frames combined (frames blended). The effect is progressive, even if the NLE sees the footage as interlaced. It only matters if you actually can visually detect interlacing when the footage is being played.
I hate a lot of the "nomenclature" for video because it's very distracting. 60i is almost always, technically 59.94i and 60 anything almost always means 59.94 frames per second whether interlaced or progressive, just as 30 anything almost always means 29.97... except... nle's can produce exactly 30 frames per second. It's just easier to say "60" and "30" so we don't have to keep stating the decimal portion. And as for uploading to youtube; doesn't matter... 29.97 or 30, your choice (I use either, but more 29.97 these days because that is the "proper" 30 for video [confused yet?])... but the best results will be with progressive footage.
Why not 1080/60p? 1080/60p is available on some higher end (and/or newer) camcorders/provideo and is not AVCHD format. Most consumer camcorders use some flavor of AVC and only AVC and therefore, 60p is not available (because it is unsupported in the specification.) [lower resolutions like 720 and 480 have 60p support in the AVC spec. Again, it will almost always actually be 59.94p.]
FCPX is a little schizo when it comes to interlaced material. Sometimes you see it, sometimes you don't (depends on project settings.) In general: FCPX will try to conform your video (from 60i) to say: 30p, 25p, 24p, whatever - basically: 60 -> 30 will jam 2 frames into the one (frame blending). If you play your XXi footage in your project and you perceive interlacing? Go to Inspector > Info > (@bottom left of pane select) Settings and adjust the *field dominance override* [in general: "Lower Field first" is *usually* what you should set] to eliminate the interlacing effect.
If your project is progressive, it will export as progressive. If you're developing video for online services like youtube that want "30p", manually set up your projects for 30p (or 29.97p [almost literally splitting hairs here!]) and let FCPX pull the weight for you.
[From what I've read, most consumer cameras shoot at basically one frame rate: 60fps. The files they produce are software engineered in the camera, and for rates less than 30/29.97, the camera does not shoot 24/25p frames per second, but applies a frame reduction scheme from the manufactured 30p from 60i frames... the "cinema" effect (great marketing tool - pure BS)... some people might be sensitive to the frame reduction pattern and think it looks terrible; most won't notice and think it looks "cool". Unless your camera can shoot "true" or "native" 24fps, then all you're getting is a gimmick (IMO)... Anyway: you will get your *best* file quality from the 1080/60i (basically "raw") footage and let FCPX conform it to your project settings. You might also consider shooting 720/60p and letting FCPX upconvert to 1080... the quality is still outstanding and there are no interlacing issues.]