I had a similar story this past week. I was flying in DL J class which was overbooked. DL rebooked us into LY F. We went to the LY checkin counter and were almost fully checked in and already had assigned seats when the manager realized that they oversold their J cabin and were going to upgrade pax to F. They then denied us boarding and claimed that DL oversold LY F, which was a complete lie. The cabin was F3 when DL booked us two seats on it into F class. Then they said that they could accommodate us if we purchased full fare F tickets on LY ticket stock and then later changed their mind when we said that we would do that. They also refused to give us any compensation or a hotel voucher.
In short, classic EL AL incompetence and rude disregard for anything remotely resembling customer service.