Error creating subtask in JIRA: com.atlassian.jira.rpc.exception.RemotePermissionException: This issue does not exist or you don't have permission to view it.

Premises:
FishEye 2.7.5
JIRA 4.3.4
JIRA FishEye Plugin 3.1.5

Summary:
When trying to create a sub-task in JIRA from a Crucible review, this error is displayed in a popup:

Error creating subtask in JIRA: com.atlassian.jira.rpc.exception.RemotePermissionException: This issue does not exist or you don't have permission to view it.

What have been tried:

• Granted all possible project permissions in JIRA side for the user that's logged in both sides;
• Enabled all three authentication methods in the App Links configuration to see if it makes any difference (tried with only Trusted Applications first);
• Checked that the JIRA issue linked in the Crucible review is opened;
• Still get this error.

I'm attaching FishEye logs with extra debugging information for investigation, as well as atlassian-jira-security.log from JIRA side. atlassian-jira.log didn't log anything.