It's a long-standing myth of historical bar-trivia. I was told the same thing by a middle school history teacher many years ago. It is actually much older than that, getting its lease on life from a work of popular history called
John Hanson: Our First President published in the early 1930s.
As you state, he was the third person to hold the title he held, but it was common to refer to the position as "president" (both in official communications and general newspaper reporting at the time) and while there was no country called "The United States of America" the name of the body of which he was "president" was "the United States of America in Congress Assembled".
But it is definitely important to understand that Hanson's position in no way resembled the position of president of the United States of America as defined by the constitution. The important historical distinction to be made is that the Articles of Confederation that created Hanson's position was
explicitly designed to
not have a position like our presidency.
The twist on it here that I had never heard was that he was black. That's relatively new. Is this the picture that was included on the handout?
If so, then it looks like your son's teacher took the information directly from a
column by black comedian/social activist Dick Gregory. In it, he pretty much repeats every myth and misunderstanding about Hanson that I've ever seen. Weirdly, other than in the photograph attached and title he never mentions Hanson being black. This is somewhat amusing since another ethnic group mythologically claims Hanson as well, the Swedes. So, perhaps he was a black Swede.
A bit at Wikipedia about this suggests Gregory may have been confused by the fact that John Hanson's grandfather had been sold. But in actuality, his (white) grandfather had reached the new world as an indentured servant and had his contract sold (pretty much the same as slaves) to another before working off his term. Most people don't know that for a long time indentured servitude was a much more common method of arrival than slavery, was institutionally identical (except in that indentured servitude was for a set term rather than eternal) and was comprised almost entirely of poor white Europeans.
I would talk to the teacher but don't expect much to change. Odds are s/he has a whole collection of folk histories that she is sharing with her students.