It's from Bristol local authority's own safeguarding/child protection policies. She checked those with a colleague. However, it's a key point in many policies for protection of children and vulnerable people more generally, so the point should apply wherever the research is conducted.
The old policy for protecting vulnerable adults, for instance, was literally called 'No Secrets':
https://en.m.wikipedia.org/wiki/No_Secrets_(adult_protection). This became part of the Care Act 2014 (i.e., it's now law).
Most policies talk about transparency, openness, etc. Children must be safe to talk about what's going on in their lives and adults should always be vigilant to maintain safety.
Adults are allowed to keep children's own secrets if appropriate (e.g., 'My mum walks around naked,' which could be embarrassing or lead to bullying) but can't if they suggest a risk of abuse or an unsafe environment to the child or a vulnerable person ('I can't do my homework because we don't have any pencils at home,' for instance, might suggest neglect).
Adults should not ask kids to keep a secret, though, because that's a classic red flag for abuse. Obviously, there are some things parents will ask their kids not to tell people, which are private but not a risk to the child ('Auntie Sally is a lesbian, but she doesn't want anyone to know.'). But there shouldn't really be a situation where a teacher, doctor, researcher or trainer tells a child to keep a secret.
The Lightning Process falls into that secondary category because the 'trainers' are responsible adults with a duty of care. Researchers likewise have a duty of care and shouldn't let the trainers tell children to keep secrets about the process.
It is worrying, because how can you ensure the process is safe and that abuse isn't involved if no one in the room is allowed to talk about what happened? From a research perspective there's an additional problem in that you can't know which element, if any, is effective (or harmful).
