One of the issues is making your active health check more like a doctor's physical than "'tis but a scratch" self-reporting. But also ensuring you're not dealing with a whole bunch of hypochondriacs.
Passive health checks at least have the property that they fail servers when the servers are unable to serve, even if the active health check does not consider some subsystem in its response. But alone they can easily be fooled by really fast non-error responses.
Anyway, saying "name of brand of load balancers" solves this problem is only covering the most basic cases. General solutions are at best only the first step of the full solution. You need to think about the edges - which I suspect is what Rachel is advocating.