Yes they are well founded, though it would not surprise me if a customer service agent (as opposed to a ticketing agent) didn't know the difference. Confirmed bookings can be used to get seats allocated in many circumstances so I don't know what the blockage was there. However you definitely cannot check in unless fully ticketed. If you had been downgraded from First to CW you would almost certainly need your ticket re-issued. Now normally ticket issue is automated and straightforward, however any muck up of the booking (changed route is a favoured issue) often results in a need to reissue the ticket, and that becomes both manual and error prone. Give them a few days and then see if you are in fact fully ticketed. In particular if you can't OLCI then telephone immediately. If you hassle them enough, you can get your ticket re-issued while you wait, it can take 15 minutes or so.

A change to a booking in the same class on the same route does not normally need re-ticketing, merely revalidation, which is a lot easier.