The show declares that the "dim and murky" images broadcast of the first men on the moon is "FICTION", and goes on to claim that the "real" transmissions were "bright and clear and vivid" whilst showing still photos that were taken from the moon using a Hasselblad medium format still film camera as visual "proof" of their alleged fact. A commentator identified as "Amy Shira Teitel, Space Flight Historian" claims that because the video signal sent back from the moon was not compatible with the current TV standard, that "instead of trying to figure out some way to convert it, the camera was just pointed at the monitor", and that degraded the image somehow.
The slow scan television (SSTV) camera and transmission system was indeed incompatible with NTSC TV standards, but the fact is that the camera, made by Westinghouse, offered 320 scan lines of resolution, compared to 480 of NTSC. Contrary to Ms. Teitel's claim, NASA did in fact have a SSTV to NTSC scan converter (perhaps the first in TV history) built to accommodate the TV press. The actual truth is that the image wasn't all that bad compared to the state of the art in TV broadcasting in 1969! The camera weighed only 7.25 earth pounds and drew 6.25 Watts of power. TV bandwidth was limited to 500kHz. In other words, the TV broadcast got only a tiny fraction of the Apollo 11 budget. There is no HD video of the first moon walk because it simply wasn't possible at the time.
References: Web links were rejected. A web search for "Apollo 11 video camera" will return corroborating info. Wikipedia has an entry, including a footnote to a paper written by John M. Sarkissian that goes into great detail.