Since Cenk Uygur, the loudest idiot on the face of the planet, said this on Piers Morgan's show, and a lot of people seem to believe the bullshit, I'll clarify this too.
No, Israel does not control all of the Gazan borders.
The Southern border is controlled by Egypt.
The Southern border is also heavily fortified because the Egyptians don't want an influx of Gazans any more that the Israelis do.