This is a very interesting situation.
According to the Trail Info link on their web page, the trail has passed through various hands since it was no longer used as a railroad track. According to their history page, the last transaction transferred ownership to Joe Wilson in 1997:
In late 1995, King George resident Joe Williams began negotiations with CSX Transportation for the purchase of the abandoned rail line. In October 1997, once Joe Williams had a contract on the property, Jo Turek, Director of Parks & Recreation, wrote a letter to the KGBOS advising them that Joe Williams was willing to make the railroad property available to the county and that the ISTEA Grant remained a viable means of obtaining the trail for recreational purposes. She also offered a plan to seek a grant from the American Greenways program. The KGBOS declined to support Jo Turek's proposal. In December 1997 Joe Williams completed his acquisition of the railroad property.
[...] [Later tried to sell it to the state DCR]
In January 2002, following a request from the Virginia Department of Conservation & Recreation (DCR), Delegate Albert Pollard submitted House Bill 1339, which would authorize DCR to accept the rail bed as a gift from the Conservation Fund
which had funds set aside to purchase the railway property. The property was to "be developed as a rails-to-trails project" and "would be managed by the Department of Conservation and Recreation." The bill passed the House unanimously and DCR announced the news ("Assembly Transfers Rail Bed") and plans to integrate the rail trail into the Caledon Natural Area. Due to unexpected controversy, Pollard held a King George County town hall meeting to hear and respond to concerns voiced by the trail's neighbors. Although HB 1339 was revised, taking into consideration those citizen concerns, the Senate, under pressure, referred the bill back to Committee. It was "carried over" to 2003 and died in Committee.
In early 2006 Joe Williams and David Brickley announced Mr. Brickley's acquisition of the rights to establish a private recreational trail
on the property as an intermediate step toward a state-supported rail trail
. In June, Mr. Brickley appeared before the Board of Supervisors to explain plans for the project. Currently, an organized initiative, led by David Brickley and the Friends of the Dahlgren Railroad Heritage Trail, is underway to keep the Dahlgren Railroad Heritage Trail open as a private permit-only recreational trail, and later, with state and county support, as a public-access rail trail. Trail users must have a Trail Use Permit to access the trail.
Upon loading up the King George County GIS web page, the ownership of the land comes back to this:
Owners Name: RIDGEWOOD 2000
Address 2: 4310 RIDGEWOOD CENTER DR
Zip Code: 22192
A quick Google search of that street address reveals association with David Brickley, the man mentioned in the web page as acquiring the rights to establish the trail.
So... it seems that the ultimate goal here is to eventually convince the local residents to accept giving the trail to the state to be opened to the general public as a part of the State Park system.
There would seem to be no cogent reason for the wholesale banning of the legal carry of firearms. I expect the concern is both poachers and uncontrolled target shooting, both of which can be addressed with severe legal penalties on their own.