There's some artistic license in play there - the US Treasury will replace damaged (or "mutilated" as they call it) currency for free under certain conditions.
Lawful holders of mutilated currency may receive a redemption at full value when:
(1) Clearly more than 50% of a note identifiable as United States currency is present, along with sufficient remnants of any relevant security feature; or
(2) 50% or less of a note identifiable as United States currency is present and the method of mutilation and supporting evidence demonstrate to the satisfaction of the BEP that the missing portions have been totally destroyed.
From your description they fail the first condition - they've burned it all so they aren't presenting > 50% of a note, 0% is clearly less than 50%  and they also fail the second condition as it doesn't seem that they are carrying any "identifiable" portion of the money.
No redemption will be made when:
(1) A submission, or any portion thereof, demonstrates a pattern of intentional mutilation or an attempt to defraud the United States. In such instances, the entire submission will be destroyed or retained as evidence.
The "mutilation" was clearly intentional in this case.
(4) Fragments and remnants presented are not identifiable as United States currency.
Seems to reiterate that you have to present some identifiable remnants.
I suppose if the Embassy worker was a Bureau of Engraving and Printing representative, or the affidavits they provided were sufficient to convince the BEP that currency of x value was present, and completely destroyed etc. then the only hurdle would be the "intentional mutilation" aspect.
The "intentional mutilation" itself is illegal under 18 U.S. Code § 333:
Whoever mutilates, cuts, defaces, disfigures, or perforates, or unites or cements together, or does any other thing to any bank bill, draft, note, or other evidence of debt issued by any national banking association, or Federal Reserve bank, or the Federal Reserve System, with intent to render such bank bill, draft, note, or other evidence of debt unfit to be reissued, shall be fined under this title or imprisoned not more than six months, or both.