Back at the campus apartment, I'd sometimes sit out in the livingroom and watch recorded TV shows from my computer, sent over wireless. I recorded TV shows at the max bitrate to get the best quality. The wireless connection could barely handle the data flow without dropping frames. If the microwave went on though, I started getting skips in the video.
There's a pretty powerful transformer in there to step up the power to a few thousand volts, still at a pretty substantial amperage. That's going to throw out a strong magnetic field.
So I'd say that it's not because of microwave radiation leaking out that it's screwing with your wireless, but because of the oscillating electromagnetic field from the main transformer. That, or else it's from the magnetron itself, but still not because of microwave radiation. Old magnetic ballasts for fluorescent lights could do the same thing.
But I could be way off on this.