> If you obtain libmysql.so and use it in any way, you have to respect the license or you're in breach of copyright law.

The GPL is a distribution license, not a use license. Once they've received that source and/or binary, they can do whatever they want with it as long as they aren't distributing it. (Copying it to another machine under their control may or may not be distribution, depending on the circumstances.)

Yes, once they want to distribute their copy to others, they need to comply with the terms of the GPL. But not before then.