I do not agree. This is the usual way, but it's neither the fastest nor the most versatile. Try this:
1. Remove the end two joints of wings. Remove the wishbone.
2. Lay the bird on its side. Cut down the back, to but not through the bone. Lift one wing slightly and pull the shoulder skin back, then cut through the joint which is now almost exposed and aligned with the cut. Flip bird and repeat for opposite shoulder.
3. Stand bird on its bum, breast toward you. Grip the collar (thumb inside the neck) and one shoulder with one hand. With the other, grab the wing and the flesh on the back on that side, pull out and down, and peel the flesh down the back until you see the oyster (this is one quick motion). Repeat on the other side. Continue holding the collar with one hand. With the other hand, first two fingers in a fork, insert the fingers down the breast, one finger per side, and pull down sharply until the leg meat is on the verge of tearing.
4. Put the bird on one side. Cut under the oyster. Fold the knee and point it toward the neck naturally, then fold it out and down, cracking and exposing the thigh joint. Cut this joint and pull the meat down. Repeat on the other side. When you pull this meat down, the entire main carcass will detach from the flesh. (The tenderloins will remain on the carcass: see #7 below.)
5. If you wish to debone the legs, grab a thigh knuckle, cut around the nub, then scrape the flesh down to the knee. Cut around the knee joint, then scrape down to the ankle. Push the bone back into the drumstick to reform it more or less naturally. Either cut off the ankle with a quick chop, or, if roasting, break the ankle through the skin with the back of the knife (for roasting, this prevents the skin shrinking). Pull out the entire thigh-shin bone from the cavity. Repeat on the other side.
6. To remove the wingbones, cut around the joint, then grip the nub with the offhand and grip just below it with the thumb and first two fingers of the on-hand. Press the meat down to the board with the on-hand, and pull up sharply with the off, releasing the bone in a single jerk.
7. The breast tenderloins are still attached to the carcass, and should be removed by scraping under each with a thumb. Remove the tendon by holding its end and scraping down with a petty knife. Flatten out the bird, skin side down, and in the middle on each side there will be an empty space with skin and no flesh. Put a tenderloin on each, and you have a perfectly deboned bird for stuffing.
For Turducken, you probably do not want the chicken and duck to have all the leg meat, depending on the size of the turkey; I'd remove the drumstick before deboning the thigh, but leave the latter on. I would leave the drumstick on the turkey, and not debone it: when you get to the knee, just cut through the joint instead of around and pull out the thighbone. This will allow the final roasted product to look more like a normal roasted turkey.
Incidentally, the entire process described above takes me 6-8 minutes with a chicken. The trick is that you don't use a knife very much. Jacques Pepin, from whom I learned this technique, does the whole thing in under a minute.