Unfortunately as we are talking state grounds as opposed to public they can do what they like. Private land. Don't get me wrong I understand your rage and would certainly have publically condemned the decision but it is legal.
I believe you are completely and utterly confused, or have somehow managed to turn things completely inside-out.
Capitol Square is a public park.
http://www.virginiacapitol.gov/index.php?p=capitol_square
The public area surrounding the 1788 Capitol was originally a weed-filled, virtually treeless open square with informal lanes and footpaths. The first formal landscape plan for Capitol Square was developed by Maximilian Godefroy in 1816. His formal walkways, public fountains and trees planted with geometric precision recalled the courtly gardens of 18th century France. In 1850 John Notman was hired to redesign the landscape of Capitol Square.
Winding walkways take visitors to scenic attractions making for a pleasant walking tour of the Capitol grounds.
He introduced informal winding paths, additional public entrances and new plantings of trees in scattered groups. Notman's plan was implemented in the 1850s, making Capitol Square one of the first major urban parks in the nation designed in the English picturesque style. The current landscaping of the grounds reflects various elements of previous 19th and 20th century designs used on the Square. As a planned urban park, Capitol Square is older than Central Park in New York City.
Specifically because it
is "state grounds" - as opposed to private property -
they cannot do whatever they like. Yes, they can create rules like no sticks, poles, or other pieces of wood/metal/plastic/cardboard to attach signs to, or that you have to remain 30 feet from the Bell Tower if you are meeting in that area, or that groups need to get a permit so they can efficiently appropriate the time available for various groups to use the area. But they cannot block out "free speech zones" that might or might not be in places where the speech/activity is pretty much out of the view and hearing of the Capitol buildings or the general public using the grounds or walking/driving past Capitol Square.
Further, without objective documentation that the group applying for a permit to use Capitol Square during the traditional lunchtime would in fact keep state workers and/or the general public park from being able to find a place to eat their lunch al fresco, they cannot use that as an excuse for denying the permit application. And they cannot claim that the proposed activity will, or would tend to, or might, upset or offend or outrage or otherwise bewitch and bother folks having lunch there. What they can do is wait until there is specific behavioor that violates specific laws such as but not limited to disturbing the peace (which, BTW, does not exist as a crime in Va except under Common Law) or incite
http://leg1.state.va.us/cgi-bin/legp504.exe?000+cod+18.2-485 or riot
http://leg1.state.va.us/cgi-bin/legp504.exe?000+cod+18.2-405 et seq or use abusive language
http://leg1.state.va.us/cgi-bin/legp504.exe?000+cod+18.2-416 the Capitol Police can act to retore order.
Capitol Square is the front yard of what one of our esteemed legislators has lovingly referred to as "The People's House". I'm sorry to hear that the same does not apply in your state.
stay safe.
