The situation just gets weirder after having time to think about it.
If it was always going to get sent off for testing, she would have been told that and told to use contraception until getting the all clear. So there would be no urgency in letting her know that it hadn't worked. The wait time would have been so long that most people would have chased it up by now if they were expecting a result.
An emergency in the NHS is something life threatening, not that on that one day Sarah might get pregnant.
They did not receive the results on Boxing day, they didn't on Christmas day, unlikely on Christmas eve (Sunday) or the Saturday, for something very routine and non urgent. So whoever did get the results back had them at least 3+ days before so it could wait another day to get in touch with her. There would be no point the person rushing around emailing people to try and find out more, because there would be no one working to check those emails.
Secretaries/admin staff would not have been in work, so it makes no sense who the person was that she spoke to. Same with the doctor later. Any consultants would be more likely on call than in work full time, and are contacted about emergencies only. Not some woman who wants to know something about some results about something that happened nearly 3 months ago. There would be some registrar responsible for the whole department plus emergencies. It's a small hospital/trust and will probably be running on bare minimum staff on a good day never mind over Christmas.
They do not want to admit mistakes on the phone, especially as on boxing day the staff in question would not have had chance to seek advice on what to say. Another big reason is it leaves them open to it being recorded just like Chris and Sarah have claimed to do, before anyone seems to have any facts and information being given by someone who has no idea what is actually going on. Even if they decide it's a miracle, damaging the wrong thing during surgery could still have affected recovery, led to increased pain, have implications for a future pregnancy. If they were to say they still want the tubes tied it would then be another operation and further recovery that should have been unnecessary. So either way, the NHS trust/staff would have to approach this more formally than has been implied.
Saying that her going to hospital appointments will prove they are telling the truth - she was already supposed to have more appointments about the forgotten cyst. So her being at the hospital proves nothing. They like to hide the camera and film what they can of the children in hospital, but never for Chris or Sarah so no one will ever know why she is there.