According to the site, Oscorp has had to give up "cross-species genetics" in the wake of The Amazing Spider-Man and The Lizard's rampage through the city.
"Oscorp Industries announced today that it has destroyed any and all research it has done in the horrifying field of cross-genetics," wrote the Bugle. "This news comes in the wake of the recent sentencing of former Oscorp geneticist turned terrifying lizard creature Dr. Curt Connors. Once a pioneer in the field of cross-genetics, Connors’s work transformed him into a literal monster who rampaged across Manhattan."
With the division shut down, it seems as though we're falling well into the territory if "industrial accidents" for the villains' origins, more in line with what you ordinarily see in the comics. While Spider-Man's origin was an honest-to-goodness accident, The Lizard was an overzealous, desperate scientist stepping outside of the box--but he would have claimed it as a great success had he managed to do what he hoped to do, and it would have made the company rich.
Based on what we've seen in the previews, it seems that Max Dillon literally stumbles into a tub filled with electric eels as part of the Electro origin, and we've seen that whatever happens to create the Green Goblin, it's Dane DeHaan's Harry Osborn who gets the role. Could that be that Harry -- who is obviously impressed with the program when he says (again in the trailer) that it can "literally change the world" -- subjects himself to testing in the hopes of getting the program back on track?
Doesn't seem like too much of a stretch...