OK, I'm stupid! PHPMyAdmin HIDES all the databases apart from your own. sqlyog doesn't! You can see ALL the databases on the server but you can only access your own. It's still a security hole though. Can it be set up to ignore/hide all databases that you don't have rights on?
This is an issue with MySQL. myPHPAdmin works around it but traditionally, clients have not had to work around it as the servers have dealt properly with it.
I'm hoping that this will be resolved in the 4.x brance of MySQL but it's really not the client's (SQLyog) issue to resolve.