Anyway, creating a test outlook profile proved that this was the issue. However, you cannot change the source of the account in the existing profile. So for this support problem, I added the original accounts (there were two here, outlook and Hotmail .com) and then changed the default account, and then deleted the old ones.
Of course at this point the OST files with all the email go, and you are back to downloading the entire account history from the backend servers. Fortunately in this case the connection was fast and took a couple of hours across both computers.