Let's picture the experiment. You entangle two photons, photon A heading toward a double slit, and photon B heading in the opposite direction. Now you have two choices. You can measure photon B before photon A reaches the double slit, which will collapse the function describing both waves, breaking the entanglement. Photon A will then self-interfere normally when it goes through both slits, and you'll get the diffraction pattern. Or you can calculate it so that you measure particle B after A passes through the slits, which will mean it has already self-interfered, and you'll get the diffraction pattern.
Let me make sure you understand how the double slit works. Each time you fire a particle at a barrier with two slits, the particle-wave will diffract through both slits just as any wave would. The diffraction will create the usual peaks and troughs in the wave propagating through space (constructive and destructive interference). These peaks and troughs represent the probabilities of where the photon will end up once it hits the detector (well, more precisely it's amplitudes. Probability is those amplitudes squared). As more and more particles are fired, they all self-interfere, giving us the end results with the interference pattern. So the pattern only exists once you measure many particles and see the pattern. You can't tell anything without measurement.
Thank you.
From what I can tell, then, the guy in the video was mistaken. He seemed to think that the two entangled would either both have diffraction patterns, or both not have diffraction patterns, based on whether the was measured or not.
That explains why the physicists all left the room without asking questions.