I've only just read the article on Fox News. It sounds like the agency has crossed their Ts and dotted the I's. It reads that at least one, possibly two, decisions were issued ordering the cattle off. These were apparently upheld by at least two different judges. I'm not sure if the tortoise or non payment was the cause for issuing the decision, but regardless the permittee lost in court. The cows have to come off. He cannot pay the county as they do not have the authority to issue grazing permits for that land.
Impoundment is absolutely the last resort. The solicitor's are very cautious to suggest taking that action for the threat of TORT claims. Therefore, these types of actions recieve huge amounts of scrutiny from both sides and very likely wouldn't be taking place without all the ducks in their proper rows.
Regarding the issue of where the property lines are, which was not mentioned in the article I read, but was above. That may or may not matter. If the private land is in Exchange of Use (through a signed agreement), the landowner has abdicated grazing management for that land to the federal agency and therefore the land is managed in common with the federal lands within that grazing allotment. This is common on allotments with checkerboard ownership. The lands can be withdrawn from that agreement easily by the landowner. However, if the lands are not fenced or animals placed on that land are allowed to wander on to federal lands they are considered in tresspass.