This is entirely incorrect.
All leaders have access to training in the official programme, and where units aren't meeting it, the commissioner would then get in touch to help them to offer it properly. District, Division and County Commissioners are the chain up which issues would be escalated if there was to be a problem, and they certainly check on how groups are run (in most Districts, there's termly meetings where you're asked to share what you've been doing that term).
Leaders with Girlguiding are trained in Safeguarding. To be a qualified unit leader, you have to have completed Levels 1, 2 and 3 of official Safeguarding training (totalling about 5 hours). At any meeting or event, there must be at least one volunteer who's completed Level 3 (as well as holds a first aid qualification).
To stay as an adult at a residential with Girlguiding you have to have completed Level 1 and 2.
The onus on Girlguiding volunteers in terms of paperwork and training is actually much larger than in scouting!
OP - The way the skills builder badges work in particular, is that there's 5 activities to complete, and girls must do 4 of them to earn the badge. Sometimes these are games, or leaders can adapt them to turn them into games, so there's every chance your daughter is completing things for the badge, and legitimately playing games.
This week we started our first aid stage 3 skills builder, We started the session with one of our favourite games, then we had a discussion about different peoples needs, then we 'played a game' where girls had to run to the side of the room to say what something was a symptom of. Then we came back together for a discussion about emotions and things, then 'played a game' where girls all had to act out different feelings, and show them through their words, body language and actions. Then we finished with a quick round of a sitting down game whilst the leaders sorted out birthday cards and badges to be given out. It would be perfectly legitimate for a Brownie to go home and say 'we played lots of game tonight', but we've also signed off some criteria of the first aid badge.
I'd say contact the leaders and let them know she has started to enjoy it less since her older friends left, and she's having trouble making new friends. They should be able to work into the programme some group activities or other activities which would help her make some new friends. If she's super keen on badges, you could also encourage her to do interest badges at home, and if she's done lots of them, ask the leaders if there's any other badges she can work on in her spare time (or over the holidays)
I also know lots of units will have something exciting planned for this half term in the run up to summer hols with lighter nights.
I'd say tell her she is committed until the unit breaks up for summer, and then you can make a decision in August about whether she really doesn't want to go back, just make sure if she's not going back you let the leaders know a couple of weeks before term starts so they can offer her place to someone else on the waiting list.