That sounds right.
Free and non-free software can be shipped together. Your non-free program can
even be dependent on GNU GPL'd software. It just can't be derived from it. It
is only once your code is a derivative of the MySQL code that there is an
issue.
If there are any developers who would like to chime in on this please do.
In more simple terms, if you modify MySQL and those modifications end up
being distributed in binary form you have to publicly release the
aforementioned modifications.
Your writing a non-free application that is used in conjunction with a GNU
GPL'd program. You are not developing a program derived from that code
though.
I also want to point out that I'm NOT a lawyer and none of this is legal
advise. This is as I understand it.