You are so correct
It's the ginger, in the ginger ale, that settles stomachs, so IF one has ginger in the house, a tiny slice of it, in weak tea, is also very good; perhaps even better.
There's something/s in tea that is sort of medicinal, which helps make one feel better. A cinnamon stick and/or a slice of lemon studded with cloves, in tea, is another good for sore throats, upset tummies, adding something like electrolytes. :-)
"Beef tea" ( skimmed and strained plain beef broth ), is another really OLD FASHIONED, soothing substance for the sick.