Well, as he shows it, the frame holds the glass, but once you remove the inside part, the glass is still glued or caulked to the outside part of the frame and it takes effort to remove it. If you do remove the inside frame (which would come out as one piece exposing the large glass pane), the glass should stay in. The problem is, you never know of the door has the glass glued in, if the glue is still holding, and so on. You'll likely be fine, and yes, it would be far easier to tint without the frames in place with a much better result, but just be cautious that the glass does not fall inward. Once you remove the frame, it should be immediately apparent if the glass is going to come loose.