The "true" black frame is underneath the glass, so I doubt it would be possible to do it with OEM parts. It's not like the frame on the anti-glare, which surrounds the display from the outside (you can touch it).
Makes you wonder though... If the frame dimensions are similar, might it be possible to disassemble a glossy screen, remove the frame, and install it on an anti-glare? Might be a fun thing to try if you had access to some broken screens.