I've thought about this type of thing a lot. The way I'm looking at it now is why do that they don't have to be independent of each other? . I'm not trying to be elite at either one, just be fit and healthy.
I do Crossfit now, but I don't follow blindly and do the main site religiously. I am trying to listen to my body, rest when I need to and pick the types of workouts that I need (i.e.-strength, metcon. I don't mean skipping movements I don't like). I love the way I feel after a good Crossfit workout (and even a few days later)!
I'm also taking a one day Movnat clinic in a few weeks. I'm hoping I will learn enough to program my own workouts more. Right now my thoughts are that I will do Crossfit 2-3 times a week and try to do an outdoor MovNat workout 1-2 times a week whenever possible. I think there are also some MovNat inspired workouts you can do indoors as well.
Just my thoughts...