Just like most Yidden recognize the seriousness and complexity of the conversion process and would refer the person to a well-trained rabbinic authority, I think the seemingly innocuous act of notifying someone who believes otherwise that s/he is Jewish is is not task for the layperson.
One needs to thoroughly research the lineage of the person who has lived as a non-Jewish person rather than simply rely on claims of Jewish ancestry. This is especially critical in our day where the criteria for Jewish identity itself is in dispute by a variety of factions.
Just consider the proof required to convince the Israeli Chief Rabbinate of one’s Jewishness. I think the current standard is documentary proof of matrilineal descent to at least four generations among other things. That documentation may not even exist depending on where and when (how?) the person was born and raised.
Aside from the issues concerning marriage, bishul akum, stam yayin, basar sh-nitaleim min ha hayin, aidus, participation in the Pesach and so on, there’s even a prohibition in halacha for a non-Jewish person to observe Shabbos.
Are these the sort of issues any responsible person would approach in a cavalier manner?