I meant that adding seaweed to a cow's diet seems unlikely to increase the demand on our limited fresh water supply. AFAIK, there's no risk in running out of seawater.

Sure, but that only leads to a fresh water problem if the chosen "solution" to the transportation problem is to grow seaweed inland.

From the article: "When added to cow feed at less than 2% of the dry matter, this particular seaweed completely knocks out methane production.".

The "Transportation problem" can easily be overstated. If we assume AT is grown offshore to avoid the well-recognized conflicts of near-shore, then harvested material needs to get to shore for some form of processing and subsequent shipping to where the cows are. Given the super efficient nature of shipping goods over water (at least at low speed) at least the water portion of that route would be of little concern. Technologies are under development specifically for this purpose.

A bigger problem may be where AT can be farmed, since it is not native to US waters (except Hawaii) and permitting agencies are understandably strict about introductions.