LCDs, well, change all the frame at once. The issue isn't with the frame rate but at what happens when the device is drawing a single frame change.
Is this true? It doesn't seem like it is, if it were then we'd not experience tearing in games, etc.
The difference is LCD keeps picture until told otherwise, whole picture is emitting light. CRT has limited phosphor persistence, there is only one point/pixel being lit at any given time.
I have a "100Hz" CRT television that won't support light guns because the manufacturers decided they'd put this kind of image-"improving" technology in.
There are actually two techniques for light gun operation, one of which is "racing the beam" (unreliable in the presence of high retention phosphor) and the other of which is to draw a single frame of white squares for targets. https://en.wikipedia.org/wiki/NES_Zapper#Technical_details