A cow on grass can still get intramuscular fat or marbling, but it is less than what feedlot animals get. Yes a cow may move around more on grass than a cow in the feedlot, but truthfully a cow in the feedlot still gets plenty of room to move around. Those "feedlots" you probably see on those animal rights websites are actually pens full of animals ready to be sold in an auction right at a livestock auction mart, not at a feedlot. Feedlot pens are a lot bigger and typically roomier than the pens at a livestock auction mart.
No, marbled beef is not the meat from unhealthy animals. As I said above, marbled beef can come from both feedlot-fed and grass-fed animals. Grass-fed animals can have nearly as much marbling as a feedlot animal, it's just that it takes longer to finish (fatten up) grass-fed cattle on pasture than it does fattening up cattle in a feedlot on a high-energy diet of mostly grain.
It also depends on the breed. Angus cattle tend to have better marbling than Charolais or Belgian Blue. Both of the latter breeds tend to have leaner beef than Angus typically does, no matter what they're fed.
marbled beef is done by having the cow at the feedlot longer and feeding it cereal grains. i don't believe (in the u.s. at least) that farmers are allowed to prevent the cows from moving completely