I guess the Super Admin account is only considered an “Administrator” outside of the Network Admin area of the multisite? But all of my Roles were set to Super Admin level and they all worked except for scheduled posts. *shrug* No problems with using Administrator level Roles though.
I noticed under the Broadcast admin settings that Roles were all set to Super Admin level, which has seemed fine so far (my Administrator account is the only account managing everything on the multisite), but I tried lowering the requirements for “Broadcast scheduled posts” to a lower level and it seems to have worked.
I’m having this same problem. The original post is scheduled properly but the broadcast version is published immediately, which is a rather major issue. The publish status/date/time does not appear to carry over to the broadcast post.