From Hansard, it seems that Emily Thornberry has also exposed the diplomatic immunity canard:
Finally on the question of immunity, if the protection enjoyed by spouses of Croughton employees is so clear-cut, why did it take the UK embassy three days to assert it in respect of Mrs Sacoolas? If she and other Croughton spouses do, as the Foreign Secretary said, enjoy full diplomatic immunity under the Vienna convention, why was Mrs Sacoolas’s name never placed on the diplomatic list?
So she caught Dominic Raab in a blatant lie and things go back to normal. It's a joke