Indeed. There may be a toxic or stupid management culture at that company if they're worried about someone going down a rabbit hole to learn. In my experience this is usually in teams that are run by people who don't have technical ability.
Sometimes people are just frustrated and spinning their wheels, or doing work that turns out to be pointless because they failed to understand something which would have been clarified by a short conversation.
If someone hasn't pushed something in a week or two, that's a good time for their mentor to initiate a conversation and see where they're at and when they think they will push something.
Anything else is micromanagement by a company that has hired someone without giving them any amount of runway to actually work and learn the space they're in. You can also tell on company hardware and on company accounts if the junior's browsing history represents getting better or just resting on their haunches because they want someone else to do the thinking. Let's not pretend the micromanagement cultures where "fear of rabbit holes" exists are not already doing this.
Are you saying the mentor should actually go and check the browsing history of one their engineers to verify whether they've actually done "correct work" or what are you trying to say exactly? This sounds to me like micromanagement of the highest order.