I have been following this idea and I think the intention here is to cultivate togetherness in families and not question their honesty. Money is just the object to motivate parents to achieve that togetherness by fulfilling set tasks to actually do it for themselves and the family.
However, to make the whole process transparent, for example: The supervisor may ask questions about the readings from the parent: what was it about, what aspects did you find interesting?
and may ask the child : did you like the story read to you? what did you like about it? would you like your mum or dad to read more to you?
Also, since Gamification is involved, I think the set tasks will tend to be more of a nature that is measurable and accountable.