The system clearly prevents the gate agents from moving you from a BE seat to MCE. They get some kind of notice that makes it clear you're in a BE seat and are not allowed to switch.
To sum up a BE fare will only get a MCE seat if all other seats are occupied at the time of seat assignment. That's why it's better to wait until around T-1 when it's possible that only MCE seats are left. Albeit it will likely be a middle MCE.