MP4 and MOV were developed by Apple Computer for their format types. It is a container. Yes! I agree that all containers should be compatible with all formats. But that is not the way it is in the real world.
VLC is NOT a Direct Show player it uses its own libraries to decode media files. What this means is that other players codecs will not effect VLC's operation. Nor will VLC effect another player. So the presents or absence of Quicktime will make no difference to the file types or formats that VLC will support. The only exception I am aware of is WMV where WMP 10 is required for VLC to use this format and only under Windows.
VLC is not as dependent on container or file types as other players are and will attempt to play more combinations of formats and containers than any other player out there. However when it comes to transcoding you must know your native combinations for other players to have some kind of compatibility. While VLC may play these, other players may not be able to.
The MOV container is not as versatile in this regard as some others like MPEG-PS or MPEG-TS or even Matroska (MKA & MKV). Now I'm not saying there is something wrong with the MOV container, however the MJPEG format in this container is rather unusual and I doubt that QuickTime supports this natively. However the MJPEG in an AVI container is more what I would expect. But again I do not believe QT will support this natively, but WMP will. WMP and QT will support either MOV or AVI and MJPEG but this will require some third party support for both players.
I truly hope that it is clearer this time.