In New Zealand every farmer I've ever met (and I've met many) let their cattle feed on fresh pasture almost entirely. We are blessed with lots of land per person, and lots of rainfall, perfect for growing grass. In the dry part of summer or the cold part of winter when fresh pasture isn't growing fast enough, they supplement with hay and silage (both produced from fresh pasture that is typically harvested at the beginning of summer).
But I know that outside of my own experience, other things are occasionally fed such as waste products from food processing, brewing, etc. And I know that when you sell animals you can legally tick "grass fed" as long as the animal has had access to pasture, regardless of what percentage of their diet actually came from that pasture. So it is possible that some cattle from NZ have eaten mainly non-grass foods, but in practice I've never actually seen that happen.
As for seaweed, we have a lot of coastline so we could utilize this strategy more effectively than the US could.
I mean, I'd guess it was, but equally it could be "why do you care, it tastes good", so ...?