NTSC is 525 scan lines, but only 486 of those scan lines actually make it to an NTSC monitor (the remaining lines contain sync information, time code, closed captioning, etc.). Most CRT TVs overscan the image, which gives us approximately 480 lines of actual viewable resolution.
The problem is that 480p really isn't NTSC, a 50-year old broadcast standard for interlaced rastering. Rather, it's a specification of the CEA-derived term "EDTV". It scans an NTSC or PAL (in the case of PAL, we have 576 viewable lines) signal progressively. In the case of the Wii, all it's really doing is bypassing your digital TV's built-in de-interlacing by progressively scanning the video prior to output. In theory (but not always in practice), this will yield better video quality. Progressive-scan DVD players essentially do the same thing. The video itself STILL starts out interlaced on the actual disc because it has to adhere to the NTSC-D1 (720x480) standard.
Perhaps your capture card is looking for a native 525/480i NTSC signal and not a de-interlaced one. I'm pretty sure there's a way to force 480i output even over the component video output of the Wii. Check the system menu. The true advantage of using component video over composite is better color resolution, NOT progressive scan. Computer monitors and digital TVs HAVE to de-interlace (progressively scan) anyway when an interlaced signal is present. And with modern electronics, you'd be hard-pressed to see a difference between 480i and 480p material on a computer monitor or digital TV.