Unfortunately, they are right.
Last year, your income would have been £73,000 -way over threshold.
You are seeing it as follows:
If DH loses his job, my income is all we have. That means we have an income of £13,000 per year.
However, as we are in August, we are already 4 months into the financial year - 1/3 of the way through. 1/3 of your DH's income is c. £20,000.
This means that your income for this year will be £20,000 + £13,000= £33,000 - over the Child Tax Credits threshold still.
What is unfortunate, is that you have had your income 'front loaded', in that 3/4 of your income (if your DH goes out of work and stays out of work) has been paid to you in the first 1/3 of the year.
Incidentally, on a household income of £13,000 per year, you wouldn't qualify for Free School Meals. You have to be either on the top rate of Working Tax Credits (which you won't qualify for) or on JSA.