Possible, but unlikely. If it was the 9608 user then it shouldn't show that digit 6 was pressed on monitor, if it was the door phone user then the other phones wouldn't work with it either. No harm in deleting and recreating one or both of them to see what happens though.
If you have one phone that doesn't work side by side with one that does, then try swapping one element at a time and see at which point the fault moves. Start with the switch port, then the cable, then the actual phone buy logged in as the original extensions, then the extension but hot desk into the original users, and then finally the user. At some point it must move from one position to the other, and then you have the cause. Once you know what is causing it it will be much easier to work out a solution.
Joe Newton