Yes, that is correct. You do have to be logged into a family site as a site manager in order to see the delete a tree option.
Esther / MyHeritage Team
Once you have logged into the family tree on the site,
Click tab (Family Trees) - select option "Manage Trees"
Beneath that in the box, you should see something similar to this
# | Family Tree | Source | Language| Individuals| Last Update | Actions
1 Exported GEDCOM English 241 03/15/2009 View
Pick the correct tree and click delete (See attachment)