A role just for taxonomies

I have this problem.

I need and I have a custom role just for managing taxonomies, these taxonomies belong to different custom posts that I also have.

For example I have the custom posts Product and its taxonomy Product Type. In the WordPress Dashboard Menu it shows Products -> Product Type.

But the thing is that when I log in to the WordPress Dashboard with this role I can’t see in the Menu the products which has just one taxonomy. But those products which have more than one taxonomy appear.

I’ve already installed Admin Menu Editor plugin and I can see the capabilities I set are OK. Also when I add another taxonomy to those custom posts who have one taxonomy just for testing, they do appear in the Menu.

I can’t figure out what the problem is. Has anybody had this problem before?