Very good reasoning. It's always good to be wary of these so-called experts the world is full of.
However, I do think you're in fact falling for the experts that are trying to demolish homeopathy.

People pop-up homeopathic pills (plain water) and believe in the whole thing because "experts" reassure them of the positive effects in at least 33% of the cases.

As far as I know most experts from the traditional medical establishment are against homeopathy and I've read countless articles that those pills are just sugar. I used to believe that myself and looked down upon people that gave such pills to their children.
Until my own child had a bad reaction taking common pain relief medication and I was forced to look for alternatives. It's been years since I've been treating my child with homeopathic pills whenever he gets a cold. I use such pills myself. To use your own rule of the thumb, there are far more experts saying I shouldn't take sugar pills.