"Create Sub-Task" does not show sub-task issue types when called from a gadget's drop-down menu, when Quick Create is enabled

Reproduction Sequence:
0. Have Quick Create/Edit turned on (by default)
1. Create a dashboard with a gadget that displays a table of issues, say, "Assgned to Me".
2. Use "gear" action dropdown on a non-subtask issue and select action "Create Sub-Task"

Observed: a new pop-up dialog with Create Sub-task form – however, the Issue Type: field lists all non-subtask issue types.

Expected: sub-task issue types in the selection field.

One can proceed with creation of an issue, but it won't be a sub-task, but a regular issue - according to the selected issue type.

From what I can see, the problem is that parentIssueId is correctly extracted from the iframe context and not passed to the server.

/The same problem happens in the Structure plugin, so I hope one fix will cover it all./