It's basic probability -- those slices of cheese actually are explaining, in effect, multiplication of probabilities. And we need to do is simple pairwise comparisons.
So, let's take 2 scenarios: (A) chap persuades women to plant camera, as compared to chap plants camera himself (B). In a mixed sex loo, the first one has a LOWER risk (to us) because everything else being equal, he has to persuade someone else to do his dirty work for him. So, A safer than B in a unisex loo scenario. This DOES NOT assume there aren't additional factors, such as problems doing the DIY, wandering in with power drill, pretending you're a contractor, putting your foot down the loo whilst trying to stand on the seat and trying to get the camera up in the ceiling void or whatever else our camera fixer is doing. We just need to assume they act equally for him and his female accomplice.
But unisex STILL says A safer than B. Female accomplice scenario less risk to us than chap plants camera himself.
Now make the loo female only. Makes scenario B (chap plants camera) EVEN RISKIER for the chap, hence SAFER for us. But doesn't do anything for scenario A, which was already safer for us. So, WHICHEVER thing he choose to do, do it himself, or try to persuade a female accomplice, having a female-only loo is STILL the safest for us. This is BASIC probability, because of course what you really need to do is not take just ONE offender and ONE occasion, but ALL would be offenders and ALL scenarios. And having a single-sex loo is SAFER on average, because it either doesn't effect the risk (female accomplice or even offender in unisex or single-sex loo), or makes it riskier for the offender (male in either unisex or single-sex loo).
The logic is actually simpler than even this -- the ONLY question, whatever the sex of the offender, is would letting males into a former female only loo magically protect us or not? And if so, HOW would that work.............