One scenario, and I think what people were paranoid about, is that you could make your cuts really arbitrary, and select a region where you by accident have too few simulation events and too many data events - say "Select all events where the first muon has momentum > 15.6 GeV, but not between 20.1 GeV and 20.3 GeV, unless there are 3 jets, in which case the selection is...". You just try out so many regions until you find something. For this reason you need to keep every step of your analysis justifyable, and a BDT is somewhat more explainable than a neural net (it's essentially just a trained list of simple cuts). Another thing that is frequently done is a blind analysis, where you only look at the real data when everything is finalized and locked in.
There are other issues beyond cherry picking that determine which methods you can use. E.g. the simulation doesn't reflect all correlations between variables, and it doesn't simulate the hardware triggers perfectly - so your simulations might behave different wrt. certain cuts than your data.
Nevertheless, it is not like you are banned-banned from trying different methods. When I was in particle physics (ATLAS and D0), we tried all kinds of creative things including NNs. But you have to convince hundreds of collaborators to put their names under your paper and you have to pass internal peer-review, which can feel a bit conservative and frustrating.