Mmh... The GPL and copyright are about information distribution. You, as someone who owns their copy of libmysql.so and libproprietary.so, can do whatever you want with them. They're on your hardware and no one can tell you what you can order your hardware to do with the information that's on it. The question is, if you write a program that uses them both and you share that program with the world, how are you supposed to license that program? I.e. What rights are you supposed to give the users of that program?
So the question of whether you've broken copyright law depends on how you've licensed the program that links to both libmysql.so and libproprietary.so. If the program is closed source, then yes, you've broken copyright law. If the program is GPL'd then, I don't know. Maybe you have, but I don't know who could sue you for making a GPL'd program that depends on a closed source library that you don't have the source for.