Premiere Elements does need Quicktime in order to work with a number of key file formats.
Fortunately, an expert at Premiere Elements support site Muvipix.com says that the vulnerability in Quicktime is only a danger if you use it to play files. Simply having it on your machine won't harm your system.
I'd recommend that you keep Quicktime on your computer -- but that you set up another player (I like VLC Media Player) as your media player so that you never have to actually open it.
But if APE use it in the background our systems are in danger ... ?
And why keep it if APE don't use it ? I only have it on my PC because APE installs it when you install APE. And I thought APE uses it for previewing in the timeline while editing (in that case it is ofcourse essential .... !) but maybe I'm totally wrong on this.
So if you receive more info on what moments APE uses it please let us know so everyone can decide for his own then.
You do need it to edit many video formats in Premiere Elements. But apparently you can disable the program itself (the QuicktimePlayer.exe file) and still get the benefit of the codecs the program provides.
There is no danger in using Quicktime as support for your video editing programs. The only vulnerability, as I understand it, is in using the Quicktime player.