I can’t find it quickly as to whether it might be true, but another possibility is that the Inn was built pre park. When the park came they offered the owner leases for long stretches of time.
I do not think that is the case here since this inn looks 1960’s-ish and the parkway was already there. But it could be. Elkmont in the Smokies had a slew of vacation homes that had such leases for upwards of 99 years, IIRC.
http://www.pisgahinn.com/history_of_pisgah_inn.htm
It was built in 1974 and the lease is/was apparently up in 2013. I don’t see how that still gives federal authorities the right to shut it down.