The situation is, probably, a bit different if the video player authors have no intention of using GPL code and just develop an interface, and someone else unrelated comes along and writes a GPL plugin. But if the app's authors ship the GPL plugin or worse write it, they're on shaky ground.
(This gets you into some slightly silly situations where author A writes GPL software A linking software B, software B can make use of a GPL-incompatible library C, all of A, B, and C can legally redistribute their software on their own, but Debian has to make sure A doesn't link C because they're shipping the whole thing.)
Sort of. If you license your main source code under, say, the MIT license, you can distribute that source code, and any object code compiled from it, under the terms of the MIT license.
However, once you distribute a binary containing that source code and some GPLed source code linked together, you have to distribute all that source code (including any other libraries) under GPL-compatible licenses, such that the user can compile and distribute the application themselves.
The LGPL allows you to keep your main source code closed-source while using an LGPLed shared library, so long as a user can replace the shared library with their own version.
See the discussion of libnoreadline.a in this email exchange: http://clisp.cvs.sourceforge.net/viewvc/clisp/clisp/doc/Why-...
and specifically Steve Jobs asking Richard Stallman if he could avoid having the Objective-C compiler be under GPL:
I say this based on discussions I had with our lawyer long ago. The
issue first arose when NeXT proposed to distribute a modified GCC in
two parts and let the user link them. Jobs asked me whether this was
lawful. It seemed to me at the time that it was, following reasoning
like what you are using; but since the result was very undesirable for
free software, I said I would have to ask the lawyer.
What the lawyer said surprised me; he said that judges would consider
such schemes to be "subterfuges" and would be very harsh toward
them. He said a judge would ask whether it is "really" one program,
rather than how it is labeled.
I am personally not a fan of that answer, but between recent caselaw like Oracle v. Google and some clarifications in GPLv3 around "Standard Interfaces" and the aggregation clause, it seems like betting on any other answer is a bad plan.