CenterRight has hit the nail on the head. If the public is providing money in any way, shape or form to support the event, it's a public event. Whether the money comes from the state government or the federal government is immaterial.
On other threads, madg has complained about how the BSA, as a private organization, is not intitled to free use of public facilities, so neither is GLSEN. I'd like to know if GLSEN has used public facilities at no charge for their conferences or meetings at any time during the past 12 years.