Callers can record their greeting internally ok. If they call externally from the PSTN and try to record their greetings, Unity does not record the greeting.
You mean they go through the greetings conversation and record the greeting but Unity doesn't record anything I assume... sounds like a one way audio issue - I assume they can also not record messages via the PSTN? If not, explain what you mean by "Unity does not record the greeting". If so, did you check out the one way audio tip here?