It’s a bit of a ridiculous restriction, but it seems that the OP’s daughter has broken the rules by using a gifted ticket.
On the other hand, Northern are asking passengers to transfer supposedly untransferable complementary tickets to their travelling companions if they were travelling as a group and claiming on the others’ behalf. My parents have travelled together and claimed complimentary tickets, both of which have been issued to “Mr Lyndhurst Senior”. Luckily my mother wasn’t penalised for using hers, although the pair of them were travelling together again when she did so.
If the OP’s daughter had been a male then I very much doubt that the ticket inspector would have questioned her if she was indeed the “Mr X” named on the complementary ticket.
She could have said that she was previously travelling as a group and it was Mr X who put in the claim and chances are she’d be believed, but by being honest about how she got the ticket she’s been penalised.
I’ve accumulated a pile of these tickets, some with my name on and others blank, and I’ve now got no recollection of when and for what reason each one was issued, whether or not I was travelling alone or part of group.
Anyway, none of this is of help to the OP’s daughter, who I think has been very unlucky but is is probably best paying the penalty fare unless there is some technicality in the paperwork that she can get off on.