The only medicinal reason for strong black tea for goats would be in the case of rhodi poisoning, otherwise I would have thought that a caffeine boost may the reason? I think some of mine would love it, especially my big old BT type girl, who started the craze for hot water with molasses in...mmmmhh, and now several of them like it!
Camomile and peppermint are both soothing for an upset stomach - for both goat and goatkeeper... I have given camomile tea with honey and a bit of bicarb in as an emergency electrolyte solution, the goat kid loved it!