Woman collecting signatures at library asked to move

Lois Shelton, a Missouri woman trying to collect signatures for a petition outside the Columbia Public Library, was asked to move by 3 police officers. Apparently the library has designated three spots where signature-gatherers can stand, and Shelton was not in these areas. This article in the Columbia Daily Tribune quotes a “constitutional law expert” who makes some puzzling statements:

‘”There is certainly an argument that a library is meant for patrons’ use and is not necessarily a public forum.”‘

Is there a difference between patrons and the public? Is “use” only reading but not congregating or talking?