Virginia owned it before there was a federal government!
Who would they have bought it from, King Charles prior to the revolution?
Regarding Fort Monroe,
“After the War of 1812, the state of Virginia gave the Federal government 250 acres at Point Comfort to build Fort Monroe and 15 acres at the Rip-Raps shoal off Old Point Comfort to build Fort Calhoun. Construction of Fort Monroe started in 1819, the state agreed to donate the land in 1821, and the deed transferring the land to the Federal government was finally executed in 1838.2
The Rip-Raps shoal was enlarged with heavy rocks and new land was created above sea level. Fort Calhoun was constructed on top, so the cannon of that time could control various shipping channels.
To expand Fort Monroe on Old Point Comfort, the Commonwealth of Virginia sold 31 acres of submerged lands underneath Mill Creek to the Federal Government in 1908. The sale recognized that the owners of oyster leases would have to be compensated.” http://www.virginiaplaces.org/boundaries/accretion.html
With regards to Fort Sumter,
I stand corrected as it seems the feds bought that land from SC when it was empty and semisubmerged. http://civilwarhome.com/sumterownership.htm
The federal government owned it while Fortress Monroe was active.