In the past I've had a lot of trouble with schedule changes since the agent would sometimes only rebook where the same booking class existed, or "something similar". So they might have denied me a flight even though there were seats in Y if my ticket was T. This seemed to vary case by case though, and depending on how attractive the alternative flights were.
I got so tired of these schedule changes since if buying tickets 11 months in advance there was almost always at least one schedule change - and with my LH flights always being a connection flight, then I would end up with hours and hours in FRA/MUC, or departures six hours different to what I booked.
The worst case was a schedule change to make me leave paris hours earlier than booked, but then the original flights were re-instated but the agent flatly refused to rebook me onto my ORIGINAL flights, saying she was 100% sure they would be cancelled (what is this status "will be cancelled"??). The original flights were not cancelled, but I had to put up with the alternative flights and leave paris earlier than I wanted.
Now I moved almost all my flights to BA and take direct flights finland-uk instead of with LH.