Number 018 http://www.faqs.org/faqs/apple2/faq/part16/
The fact that they suggest passing it through a VCR to use its "stablilization logic" suggests that the Apple II's composite video output is less than perfect for input to modern TVs. It is possible that the video circuit was designed around/optimized for the composite monitors they sold. I don't know enough to say, but I would not be surprised if what you say might be true about the filters is true. I think it might also be true that there is RF interference between your computer and the TV. Any chance you could describe what the problem is like or link to some pictures?