Concerning state parks (and that means state parks only, it does not include state forests or other state-owned land), the lady is technically correct. As it stands right now, until the DCNR regulation prohibiting firearms is brought into comportment with state law, open carry of firearms (i.e., handguns) is prohibited in state parks.
Any carry is prohibited in state parks per DCNR regulation:
17 Pa. Code § 11.215. Weapons and hunting.
The following activities are prohibited without written permission of the Department:
(4) Possessing an uncased device, or uncasing a device, including a firearm, archery equipment or slingshot, that is capable of discharging or propelling a projectile, except as provided in paragraph (2) or (7), or except in the owner’s building on a leased campsite, in the owner’s residence, or in the owner’s vehicle or trailer.
This total ban, however, was overcome by a tweak to state law permitting concealed carry:
18 Pa. C.S. § 6109. Licenses.
(m.2) Inconsistent provisions.--Notwithstanding the provisions of section 7506 (relating to violation of rules regarding conduct on Commonwealth property), 75 Pa.C.S. § 7727 (relating to additional limitations on operation) or the act of June 28, 1995 (P.L.89, No.18), known as the Conservation and Natural Resources Act, and regulations promulgated under that act, a firearm may be carried as provided in subsection (a) by:
(1) a law enforcement officer whose current identification as a law enforcement officer shall be construed as a valid license to carry a firearm; or
(2) any licensee.
The DCNR regulation itself is in violation of state law, but hasn't been legally challenged or amended:
18 Pa. C.S. § 6109. Licenses.
(m.3) Construction.--Nothing in this section shall be construed to:
(2) Authorize any Commonwealth agency to regulate the possession of firearms in any manner inconsistent with the provisions of this title.
Concerning Philadelphia, the lady is wrong. Any carry, whether open or concealed, is permitted in Philadelphia as long as one possesses an LTCF or is exempt:
18 Pa. C.S. § 6108. Carrying firearms on public streets or public property in Philadelphia.
No person shall carry a firearm, rifle or shotgun at any time upon the public streets or upon any public property in a city of the first class unless:
(1) such person is licensed to carry a firearm; or
(2) such person is exempt from licensing under section 6106(b) of this title (relating to firearms not to be carried without a license).
The reason Philadelphia is "special" dates back to when the Uniform Firearms Act was first being implemented. In order to get the Philadelphia representatives to agree to standardizing everything statewide and eliminating local laws, a special exemption was made for Philadelphia. Could this exemption for Philadelphia be challenged in the courts under the equal protection concept? Probably, but someone with money and standing would have to do so.