I presume they mean "use the LGPL/GPL version of Qt for your project" (out of context, you might misread it as choosing that licence for your own work).
There are no restrictions or obligations placed on you if you licence your own code as whatever (since you still own the copyright), but there are restrictions and obligations if you want to use Qt under the LGPL/GPL.
I guess they want to avoid the problem where someone uses the LGPL or GPL version of Qt thinking that means they can do what they like with it, when actually they can't.
Yes, consulting a lawyer would be a good idea for writing commercial software - but then, consulting a lawyer would be a good idea if you were using the commercial version of Qt too!
Any commercial licence (including Qt's, I imagine) tends to be complex, and places restrictions and obligations on you, and it would be best to consult a lawyer. So it's unfair to say the GPL is worse than proprietary - I guess it's just there for people who mistakenly think that GPL means public domain.
It's also worth noting that Digia make money from the commercial licensing, so it's in their interest to discourage the GPL version
As for GPL vs BSD debates, I find these a bit tedious. Pick one you prefer. Neither is "better" - the BSD gives more freedom for distribution, but the GPL is about preserving freedom for end users. I don't get why some people look down upon the GPL, when the vast majority of software is under proprierty licences, which are restrictive for both end users and distribution. If we want more open source, then I'd argue efforts should be focused on those who release closed source software, rather than in-fighting as to what the one true licence is. The flip side is to realise that people still have reasons for wanting to release closed source software - but those apply to people choosing the GPL, too. (E.g., if Qt was available under BSD, Digia would have far less opportunity to make money - why should they be criticised, when many commercial libraries don't have an open source version at all?)
Servant of the Lord is correct about the history of Qt. If you're going to complain that Qt should be under something like BSD rather than GPL, then you might as well criticise every commercial software for not releasing their code under _any_ free licence, let alone BSD.
I also don't see how this kind of arguing that everyone should release software under the free-est licence possible is any different to the GPL "agenda" of wanting everything to be free, that the GPL gets criticised for...
What you read is correct, in that the GNU system is distinct and does not always play well with other systems.
This is not distinct about the GPL, there are many issues in Free licences where some licences are not compatible (e.g., some of the various Creative Commons licences).
The ultimate problem is that there is a paradox - one cannot both have the freedom to do what you like with code, and also preserve freedom so that something remains free, since there is also the question of "freedom to make it non-free". The paradox is part fundamental logic, and not because anyone wanted to make something that didn't "play well with other systems". There is no right answer - just pick which you prefer.
The GPL isn't the only open source license - there are others. It's wrong to equate discouragement of using the GPL with a general discouragement of open source - just pick a different open source license instead.
Although note Digia are talking about which licence to use Qt under, and there aren't other open source licenses it is available under.