What was the true genesis of the Cartesian "Cogito"?

I recently read an account which suggested that the inspiration for Descartes' famous axiom, "I think, therefore I am" was actually suggested by a little-known relative, Hippolyte Marius Descartes. HM was apparently fond of claiming, as a sort of dinner-table conversation piece, that he could cause himself to shit just by thinking about it (dinner-table conversation was evidently somewhat less refined in the 17th C). Musing on this, Descartes was inspired to philosophise on the theme "cogito, ergo caco" (I think, therefore I shit).

Informed by his publishers that this would not do for a published text, he amended it to the more familiar form.

Can anybody help me with references to support this account?