I like some moisturizing body scrubs too, but it should not leave behind an oily veil on my skin. I use body scrub products to clean and exfoliate my skin, not get oiled up.
I also don't like body scrubs with very coarse, large granules. They irritate and over-dry my skin and I don't feel that they clean as well as scrubs with fine granules do.
One solution I've found for this problem is using face or hand scrubs instead of body scrubs in the shower. Face scrubs tend to be more gentle and have smaller granules in them. If I have a face scrub that's not working for my face, I put it in my shower and use it as a body scrub. It's essentially the same thing anyway.