Some of this is correct, and some of it is myth. Source: I was there ;)
Qt way back in version 1 was merely “free for non-commercial use” and shipped with the source code. KDE was founded on that version. This was in like 1996, before KDE even had a stable release. Gnome was founded immediately in response, choosing GTK (the Gimp Toolkit) which wasn’t really ready for use as a full fledged desktop toolkit, but existed and the license was friendly. KDE and Trolltech formed a few agreements – the first was the creation of the QPL, an attempt to create an open-source compatible license for Qt, and the second was the creation of the KDE Free Qt Foundation (it said, effectively, if Qt were to become closed, the most recent version prior to that would be released under the BSD license).
However, the damage was done. Stallman and others would never forgive KDE for choosing a not-free-enough toolkit, and the Gnome devs were associated with redhat. That meant Redhat and Debian, the two biggest distros, defaulted to Gnome. Ubuntu just adopted Debian, ergo Gnome.
Qt would shortly thereafter be released under GPL, GPL3, and LGPL. There’s still a commercial license option, and that pisses a lot of people off for some reason. But it was never a risk to KDE or the community – not since before KDE 1.0.