Everyone can see tables?

From my reading of previous posts here, and a bit of experimentation,
I have concluded that if user A creates a database, they cannot
prevent user B from being able to see all its tables and other
objects.

All A can do is not grant B the right to select from his tables.
B can not only see the tables, but see their structure. The same goes
for views, B can see the code behind views owned by A. I assume the
same will hold for functions.

Please somebody tell me I'm wrong about this!

I want to set up a multi-database, multi-user installation, where
users cant see metadata that is none of their business.

regards

Richard