Let's go into the Bundy case here. His family has had grazing rights over this land in Nevada for generations. Then in 1993 the federal government restricted access to much of that land to protect an endangered species. They seized the land but he refused to sell, continued grazing, and stopped paying his grazing fees. He could have challenged the seizure in court, but he did not. He could have kept paying his grazing fees, but instead he went to court and tried to argue he should be allowed to graze for free. When he lost, he continued grazing his cattle there and refused to pay for it, at which point the government took his grazing rights for lack of payment.
Whether or not grazing fees count as private property is actually irrelevant. He lost his grazing rights by refusing to pay for them. If he had kept paying, and actually challenged the seizure and sued, that would be an interesting case, but he did not.
There are interesting argument here, but Bundy is not the one making them. He doesn't even acknowledge the authority of the federal government, and instead fell into the crazy Sovereign citizen crowd.
(Also, even if grazing land is considered private property, the federal government could seize the land: https://www.fws.gov/refuges/realty/faq.html )