I'd agree - after a period during Covid where there were only very few ticket checks, SouthEastern (SE) appear to have returned to them with a vengeance. All trains from Newington will have a "conductor" (I use the generic term), and they ought to have been visible on the platform, either at Newington or the next station. I have also known people to knock on the back cab door. However, it's worth noting some conductors will focus on doors only until past Rochester or Bromley, so they can to the entire check in one sweep. However, as the PF was issued at 07:32, that seems unlikely here.
I suspect this is because SE operate a penalty fare, Newington is (I believe) a penalty fare station, and the ticket was purchased after the train left, so was not held when boarding.
That seems very soon after the train departed (i.e. she didn't make active attempts to find the conductor on board, just on the platform), but then at the same time, very harsh to issue a penalty fare. Did your daughter attempt to find the guard by walking through the train, or only at Newington? The next station is Rainham, 4 minutes away, so the conductor could plausibly have "disappeared", but not for very long (your daughter would have basically been at Rainham when the confirmation came through).
I've not paid cash using an SE ticket machine for some time, but I have seen some payment machines where they will not allow overpayment, so would 'grey out' cash as an option if it couldn't give change. Noting the appeal letter says tickets were sold before and after your daughter attempted so, could that have been an issue? Could the conductor have seen passengers with tickets purchased at that ticket machine, so reports of it not working seemed suspicious?
However, I can understand why some would regard it as odd that she wanted to purchase a ticket using cash at the station, but then paid for it online (and thus direct from a bank account) when it didn't work. There may be very valid reasons, and that's not for me/us to judge, but it's the sort of thing someone looking critically will pick up on.