Template:M summ 2002 ISDA 5(a)(iii)

Note the charming contingency that ISDA’s crack drafting squad™ allows that a counterparty might default under a credit assurance offered by someone else altogether.

Before you even put your hand up: no, a Credit Support Annex between the two counterparties is not a Credit Support Document, at least under the English law construct: there it is a “Transaction” under the ISDA Master Agreement. It is somewhat different with a 1994 NY CSA, but even there the User Guide cautions against treating a direct swaap counterparty as a “Credit Support Provider” — the Credit Support Provider is meant to be a third party.