It does look like your friend doesn't have a leg to stand on and will have to stump up for the fine.
Our lea policy clearly states
21. Should there be more than one person liable for the offence a separate notice should be issued to each person, per each child. 

22. Should the offence involve more than one child a separate notice should be issued for each child, per each parent. 

Our family could be hit with £60 X 2 parents X 4 children (£480) However, it is not clear whether the fine can be applied to each day of absence. It does however mention absence thresholds.
UNAUTHORISED ABSENCE: As the Government changed the PA (Persistent Absence) threshold to 90% (in effect from Sept. 2015), the Local Authority may issue a Penalty Notice in relation to a child whose attendance at school has been between 86% - 89% over a given period. Such a Fine is intended to offer a rapid intervention, which may be used to address non-school attendance before it becomes entrenched, following guidance in section 13.
UNAUTHORISED TERM TIME LEAVE(includes Holiday): Any parent who takes a child out of school for term time leave of more than 6 consecutive sessions over a 4 week period, not authorised by the school (under exceptional circumstances rule), may receive a Penalty Notice. Such cases will have to be supported by evidence of previous unauthorised term time leave (more than 6 consecutive sessions over a 4 week period) taken in the last 3 years and evidence of parents being warned about a potential Penalty Notice.
So ours reads that a penalty notice could be issued once a child has had 3 full days (6 sessions) unauthorised absence in a 3 year period.
It is also quite clear that any appeal has to be made to the school's governing body before the penalty notice is issued. So applying our county's rules in your friend's case, when she asked and was told no, she should have appealed then. Not just gone ahead and done it anyway.
As every parents has likely been told they could be fined (our school sent home a letter on the subject), it would be considered they had been warned of the possibility of a notice, even if there was a year between letter and absence. Which makes it even harder to appeal as the knowledge of the possibility was there.