Often people taking placebo, homeopathy, etc. will *report* feeling better - but this does not mean they are better in any meaningful sense of the word.
Curiously, I'd say that's the only meaningful sense of "feel better".
If I took treatment which genuinely cured me of some physical ailment but didn't make me feel better, I honestly wouldn't care for it and wouldn't do it again. If I took a placebo which didn't cure the physical ailment but made me feel better, I'd be all over it. I guess I'd just assumed that this was obvious and everyone would have the same reaction. Apparently you don't.
Maybe I'm influenced by endurance sports (e.g. I've done many 10+ mile swims) where I think many people can physically accomplish it, but their state of mind is the only thing allowing them or preventing them from achieving it.