FAC's consular web-site makes it clear that there are fees for replacement passports and temporary travel documents, as well as that reimbursement may be required for transportation. The only possible exception to the transportation costs would be if Canadian gov't (i.e. CF aircraft) provided the transport.
FAC is very careful about issuing travel advisories and warnings. They have a specific policy (directive) that they cannot even advise their own staff of threats if they are unable to advise all Canadian citizens. Anyone ignoring such advisories is foolish at best.
And a final point: dual citizenship is no "get out of jail free" card. Many, if not most, countries do not recognize dual citizenship as we do. Those holders of Canadian passports retaining citizenship of other countries should be careful about travel to those countries. Also, expectations of the ability of FAC to intervene should be adjusted accordingly.
What this woman went through is tough, and it was good of the Americans to put her on a scheduled military flight from Baghdad to Amman. Maybe if the timing was right, and some people knew about it, she could have caught the Op Danaca sustainment flight out of Tel Aviv. I'm sure it would have been possible had the right people been informed and had she been willing to wait. Otherwise she is on the hook for the cost.
Acorn