Last summer I had similar experience:

ARN-LHR (SK)
LHR-JFK-LAX (UA, NC class).

SK flight got into LHR with 1 hour to spare. My partner and I were paged before leaving the plane. A UA rep whisked us over to the UA check in at LHR. But the transfer took 20 minutes. At check in the agent said, "You arrived after the cut off, you can't take this flight."

Me: "I checked in with SK. According to *A, there is seemless checkin. So I expect my seat."

Agent: "You are here too late. We'll put you on the next flight through SFO in C."

(At this point, my partner says to me that this is actually better: longer C flight, better service. But I am not satisfied).

ME: "Is the flight overbooked?"

Agent: "You got here too late."

Me: "Well, if the flight is overbooked and I checked in with *A this morning, then I am due compensation."

The agent went to the sup., who then issued me two new SWU's to replace the ones we would use on this flight, and he gave us the upgrades for free.