It took 50 years before it we noticed that there might be a relation with smoking causing a lung cancer and 80 years (1980) before we were sure about it[1][2].
Acne though is far less serious issue, and not many people would be interested finding cause for it, especially since it would kill business for companies selling solutions that treat the symptoms (which do help, but you need to use them regularly)
[1] https://en.wikipedia.org/wiki/History_of_tobacco#/media/File...
[2] https://en.wikipedia.org/wiki/History_of_tobacco#Health_conc...
I don't think anyone was suggesting that it would be harmful to reduce sugar intake (although, I'm sure there may be cases where it is, or perhaps it's just easier said than done). I think it's more that there's apparently no proven link between sugar intake and acne and, given all the possible things that someone try in order do to reduce their acne, it might not make sense to choose one that has no evidence supporting it. Or at least, exhaust the other possibilities first.
Also, in the parent to my comment you say "scientists can't lock us in the cages to make sure we won't do anything else that will impact the results". But, they can, and do. It's called a controlled clinical trial. I've participated in one that went on for a week (was well paid for it) where we were kept in a room, fed a designed diet, and restricted in our activities. There were test subjects in the building who were in for much longer than my trial. So I don't think the idea that it's impossible to (dis)prove these things is accurate.
Right now the only way to find out is to try yourself, it is free after all, and you can't deny that in any case (whether it works for acne our not) reduction of sugar intake is good for your body.