Steps to reproduce:

1. Create template with at least one trigger.
2. Define template-level-tag for template and trigger-level-tag for template trigger.
3. Create a host and assign just created template to it.
4. Define host-level-tag to host.
5. Open host's trigger editing form, switch to "Tags" tab and click on the "Inherited and trigger tags" button.

Result:
See following tags:

• template-level-tag
• trigger-level-tag

I would expect also host-level-tag be inherited in case if we show template-level-tag there.