Dogeza is a pose which is kneeling down to the ground, prostrating oneself. It looks close to a bow in sitting position, but you lower your head lower and longer for Dogeza. A completely different action.
In 1868, the last Edo Shogun returned political power to the emperor, and the emperor began to rule once again. Then feudal policies such as the land-owning and "class system" were abolished and a new constitution was established. That class system was called "Shino Kosho" and the rank order was 1.warrior (Bushi) 2.farmer 3.artisan 4.merchant. Even though their rank was the second, many farmers were very poor and died from terrible famine. Due to the development of a money based economy, Bushi became poor, and some farmers and merchants became rich. "Twilight Samurai (Tasogare Seibe)" is a movie about just such poor Bushi.
Until the class system was abolished, Dogeza was the most polite way to bow to very high ranking people. Now we think Dogeza is a very humbling position, because it originated with such a distinction. So we hardly do Dogeza now. But sometimes some people do it on purpose to show deep apology or to ask big favors of others. Well it looks silly but some politicians did it on election. As joke, team mascot did it after a big defeat. A cat did it for his prank. A guy did it because he ruins the world :-p. Spider man did it maybe because he climbed a building without permission? Here is masochistic joke movie. It is funny.