Of course, the object bound to JNDI might be a factory, so they might be working with a factory, that actually produces multiple instances of the thing the client really wants.
Like, a DataSource is bound to JNDI. People access a DataSource, but not for a DataSource, but for a database connection. So, even if everyone gets the same datasource, the clients will be getting a different connection from the pool.
Okay, the connection pool presents all sorts of sharing issues as well. But you know what I mean.