Welcome, Maggie,
There is some truth to it. If, when you pick your figs, there is a milky say which exudes from the stem, they were picked to early and unripe. Some people are allergic to this "latex" which is exuded (usually only mildly so) and they get a reaction on their skin or in their mouth. Not really poisonous, but irritating. By the way, if you do not get the milky sap, it doesn't mean that the fig is fully ripe, either. There may be 2-3 more days before it is fully ripe.