I think a distinction needs to be made between topical caffeine, which has shown variable efficacy, and consumed caffeine, which can probably have an opposite effect.
Drinking lots of coffee, or any other caffeinated beverage for example, stimulates stress hormones which can lead to temporary hair fall, so I'm not sure where people could think that consuming more caffeine is a good thing. However, topical caffeine, from what I understand, conversely has been alleged to stimulate temporary hair growth when applied to hair growing areas.
My only experience with it has come combined with many purported hair growth simulators in the shampoo Revita, and that has been a mediocre experience for me thus far, seemingly slowing the rate of hair fall, but doing little else.