To clarify, Qt is entirely opensource, using LGPL. LGPL permits you to use it for free even in commercial projects, as long as you A) link to the DLL instead of statically compiling, and B) release any modifications you make to Qt's source code (not your own source code).
The licensing issue is ran by a different company (not the one who originally made Qt, and not the community), because they own the rights to license the sourcecode out at different licenses, if a commercial company decides that LGPL is unacceptable to them. Naturally, they try to push the (paid) licensing by making companies think they need the commercial licenses. They also provide services like support and things like that, as well as (probably) commercial-only modules.
Due to the arrangement of this nature, it is impossible for the company to un-opensource it, so as long as you don't mind dynamically-linking to Qt, and as long as you release any modifications to the Qt DLLs, you're fine.
If it helps put you at ease: Qt is used as a basis for many Linux distros (the KDE desktop environment is built heavily on Qt). Because of this, the Linux community pressured the original company (Nokia, the cellphone manufacturer, before Nokia was bought out by Microsoft) to release the code in a Linux-friendly / opensource-friendly library.