We've done 12 cruises on the Magic, and had DD in Club (only once), Lab (many times), and Stack (twice, I think).
DCL is very careful about their children's counsellors. Yes, they do background checks, train carefully, etc. The "no adults" policy????? They do feel that most of the time, kids do better without parents around, but I've never seen it as "no adults." In fact, in the club, almost 3s or 3 but not potty trained are allowed to "play" in the area with a parent present, but not officially participate. Also, parents are welcome to come in any time to check on their child and/or to escort them to the potty (not a bad idea for a newly trained kiddo who might get involved in an activity and "forget.")
On one cruise, there was a child who was always with her nurse for medical reasons. She participated fully, but the nurse was always in the room. On another cruise, my DD hadn't really made friends in the Lab, and was hesitant about going in alone. The staff allowed me to sit in on the activity, and even offered that I could participate....my logic was that if she got in there and made friends, she would be happy to return.
In the Stack, again...it's one of those "the kids like a private space" sort of thing. However, a couple of times, I went up to get my DD (rather than calling).
In 12 cruises, I've never seen anything innapropriate in any of the kid areas from staff. There have been occasional problems with teen boys--this was very promptly taken care of as soon as the staff was aware. DD refers to one of the teen counsellors as "a teen wanna-be." The only caveat I'd add is that we usually cruise off season, so the teen load is usually quite light (and I like it that way!)
If you have questions, feel free to pm me.