Why are compact cameras not affected by moire to the same extent as DSLR's?

I understand the issue of moire/aliasing in DSLR's is a common one resulting from the video being generated by the camera skipping lines rather than downsampling the entire image. But why doesn't it seem to be as much of a problem with compact cameras? Do compact cameras not skip lines?

The reason I'm asking is that with the moire/aliasing issues I'm having with my NEX-6 I'm just wondering if I'd be happier with a premium compact camera - even as a backup camera that I use for video. So I was trying to gauge how much difference the effective sensor sizes would be - an APS-C NEX and a 1/1.7" premium compact like the Nikon P7700.

The NEX has a sensor 366 mm sqr, the P7700 only 42mm sqr - the NEX is nearly 9x larger. But if the NEX is only reading every 3rd line, does that effectively mean we treat the sensor size as 1/3 in terms of its light-gathering capability? Which would mean the NEX has an effective sensor size advantage of 3x - but only if the P7700 is also not line skipping. Then of course the P7700 lens is at least 1 stop better than my NEX with kit lens, which makes the difference not much.

Or am I completely wrong here? (I'm happy to be corrected!).