Here's a neat major error on a 1998 Lincoln. I guess the poor thing was struck and then stuck to the die and struck again giving it a full brockage. You can plainly see Lincoln's mirror image on the other side. It's in an old ANACS holder that says "DOUBLE STRUCK BROCKAGE REVERSE - DAMAGED" I guess the "DAMAGE" must be the dents on opposing sides as I see nothing else. It might have gotten caught between the dies when it finally ejected, who knows? I've been it's caretaker for many years.
Unfortunately, ANACS slabbed what is most likely fake -- a squeeze job. A normal cent was placed between a struck cent on the reverse and some textured disc on the obverse. Here are the problems I see with this coin. 1.The orientation of a struck cent fed into a striking chamber on top of a previously struck cent will be random. But here the two busts of Lincoln are perfectly aligned. 2. A genuine sandwich strike in which all three coins are struck out-of-collar will ordinarily be much more expanded than this. 3. The texture on the obverse does not resemble the texture that would be left by a planchet. Parts of the design are seriously affected while other parts hardly affected at all. It most closely resembles the impression of a "floating encrustation", but such errors are extraordinarily rare and have only been documented in a few foreign coins. 4. It seems awfully convenient that both dies would have been completely blocked so as to prevent any die-struck details from appearing on your coin as the result of the second strike. This by no means the only fake that the major grading services have encapsulated. I've found them in slabs from all of the top-tier services, with NGC and ANACS being the most frequent perpetrators.
Very interesting theory. One point I can add is I bought and sold an 11 cent piece (a dime struck as a dime first and then somehow struck with cent dies) several years ago and both busts were aligned with each other. I have in my hoard one of these where the busts were rotated, so it does happen. Also, if it were simply squeezed wouldn't the detail be flattened more than it is here? I've seen coins like you describe and they were flattened more as I recall. Regardless, it's an interesting piece and I suppose I could re-submit it to somebody else but doubt that I will bother with that.
It's certainly true that a perfect alignment can occur, but the chance is 1 in 360. Combine that with the smaller-than-expected expansion, the odd texture on the obverse, and the uneven coverage of that texture, and you compound the number of improbable events/effects. Even if this coin were genuine, its appearance can be produced outside the Mint, and it is therefore, at best, a candidate for the suspense account. You can send it to me for a closer look, if you'd like. Who knows, I may see something under the microscope that would cause me to change my mind. It might also be worth a write-up in Coin World (I sometimes feature fakes and suspected fakes in my Collector's Clearinghouse column).
Another unlikely circumstance is the perfect alignment of your coin and the obstructing matter that covered it on the obverse face. Neither was confined by the collar, although theoretically they could have been deposited neatly over the bottom coin (the brockage-maker) by the feeder. Nevertheless, every genuine sandwich strike I've seen showed something short of a perfect alignment.