I am considering buying a wireless guitar setup - transmitter connects to a guitar's output, receiver connects to an amp's input. This is, essentially, the system we see in modern times that allows a professional rock star to run and jump all over the stage without tripping on cables. Or us regular folk to sit on the couch without our children yanking cords out.
The specific product I am looking at is here, but this question is not about this specific product - it is just an example (product recommendations are off-topic, so don't recommend. I am not asking). I am looking for an answer that covers the general case of all wireless guitar transmitters/receivers: the link is just so everyone knows the type of product I am talking about.
Looking at the product I linked above, it has some text in an image (sorry, cannot copy and paste but here is the paraphrasing): "this works with passive, not active, guitar pickups." One of the reviews states that the owner had tons of interference until he moved the transmitter away from the guitar. Searching the web I find similar reviews and statements, but nothing scientific, no clear explanation, just anecdotes. I am a software engineer: anecdotes are worthless. I want proof.
My question is: do wireless guitar systems in general work with active pickups? If not, why not, and what specific steps can I take to mitigate the risks? If they do work, why is it that I see people say they do not, and how can I avoid a situation where the two systems do not work together correctly?
The accepted answer will focus on the science or electrical engineering behind the reason, giving specific, objective reasons why the technology not a specific product, may or may not work.