This is what people post on forums complaining about: http://s28.postimg.org/xjqg6iud9/Scr...01_22_28_1.png
This is what they don't post, cause they aren't going forwards a few frames: http://s28.postimg.org/byldiwxml/Scr...01_22_48_1.png
Both from the same jump (a flip jump) and the direction of travel is basically about up the center of the screen caps (bottom to top), to give you an idea of the pivot action. Some skaters pivot more, some a little less. The jump can pivot to forwards and still be clean on the take-off. A lot of ladies skaters actually do this (Asada and Sotnikova, for example) on a lot of their jumps. Kim's flip is more similar to the one linked above - that take-off is actually conducive to a bigger jump. Some coaches call it a "power take-off." The fuller pivot sometimes work better for skaters who don't jump as high, but rotate well and want to get into their rotations ASAP.
The "full blade" jumping that people complain about (which only happens sometimes on badly tacked on doubles in combinations or by low level skaters, which are usually severely prerotated anyways i.e. toe axels), is nothing more than a screen cap of the skater's body absorbing the impact of the jump take-off. I can write a whole page on this, but I think the best way to see how ridiculous it sounds is to put on some figure skates and try to jump any decently sized double, triple, or quadruple jump off the skate rocker and not possibly give yourself a concussion after your skate flies forwards and you fall and bang your head on the ice.
You can pivot to forwards on practically any non axel jump and get no deduction or GOE fault. The judges won't even be bothered by it. They also won't think of it, because they know (many of them being former skaters themselves) what happens on a jump. There's a nice little saying among many coaches: "All jumps take-off forwards." It's true. The ENTRANCE EDGE may be backwards, but the actual TAKE-OFF of the jumps are more often than not closer to forwards than backwards.
On an axel you can go sideways or a smidgen past sideways.
There is no elite skater competing right now that I know with straight back and forward jump take offs. Not on triples and quads (or double axels). Most probably wouldn't consider it safe to jump that way. I don't personally know any coaches that teach jumping that way. Even back in the 1940s when Dick Button was doing Triple Loops for the first time, he pivoted to forwars on his take-off and many of those skaters had the same reaction with the ice in their skate/ankles on jump take-offs, because to try to stop that is to willfully risk injury (Ankle Sprains, Back Issues, Knee Issues, possibly even broken bones, and other types of overuse injuries).