I am also experiencing this. As, probably, was parker in this thread.
In our case, a major regional museum released news of significant new research prematurely, which caused some trouble.
Our system: WP 4.4.2, Broadcast 28, 3rd party pack 28.1. The post was broadcast to one other site in the network by a user with an editor account for both sites. A few drafts were saved before the post was broadcast, and the post was ‘uncategorized’ which exists on both sites.
The Broadcast Roles settings are set to ‘editor’ for all permissions.
I have been unable to replicate this on our test environment, so I can’t supply a debug dump. The user trashed the post on the child blog as soon as it was spotted. I can see that the post_date is set to the time at which it was broadcast, not the publish time as per the (untrashed) parent post. But I can’t prove that the status was ‘future’ at the point that it was broadcasted, other than by knowing that the person doing it is technically competent and was on this occasion being watched by someone else!
Possibly unconnected: when I’m logged in to the WP admin panel as an editor I see ‘Broadcast’ in the left hand menu, but when I click on it I get nothing but a PHP error:
Warning: call_user_func_array() expects parameter 1 to be a valid callback, class ‘plainview\sdk_broadcast\wordpress\tabs\Nav_Tabs’ does not have a method ‘admin_menu_broadcast_info’ in ****\htdocs\wp-content\plugins\threewp-broadcast\src\sdk\wordpress\tabs\tabs.php on line 322