See pics here:
http://www.newwave.net/~flanham/wlanham/arcade/tempOne pic is the inside of my control panel before it was finished. You can see how to join two edges together with 1x2 or 1x1 strips, screwing and gluing from the inside.
There's also a pic of the base of my Virtua Racing twin. You can see they did the same thing. Typically they used several staples on the inside, glue, and a screw or two for good measure.
The only place where strength is a big concern is around the monitor. One of the pics shows my Mame's monitor in a rectangle 2x4 frame, which is then attached to the game with 4 large carriage bolts with the heads on the outside (covered and filled, but it IMO it is okay to have a few exposed carriage bolts).
I also used some 90 degree metal brackets on the inside to hold a few panels on so they could be easily removed later - the top, the speaker panel, and the front coin door panel. I knew it would be handle if changing speakers, marquee light, or even just to lighten the cabinet if I needed to move it. The rear panels
There's just no reason to go through the trouble of screwing from the outside and filling. If you've already done it, fine, but I just can't think of any advantages to doing it this way.
Although I Lucid's design is a good one and has helped hundreds of people build a cabinet from scratch, IMHO building a frame like that is just serious overkill, extra money/work/time that serves no purpose other than making the cabinet even heavier. I built a very, very stripped down version of a "frame" for the base of my cab, and even it is overkill. You can see more pictures at
http://www.newwave.net/~flanham/wlanham/arcade , pictures are at the very bottom.
Wade