ESA and pregnancy

I've been following a generally bad-tempered and ill-informed debate elsewhere, but it led me to re-check some of my facts here and on a couple of other usually reliable sites (e.g. CAB) and I discovered that I had made what might have been some wrong assumptions, so I thought I'd check here.

Two quotations from your ESA Guide:

To get income-related ESA you don’t need to have paid any contributions, but eligibility is means-tested, so your household must have a low enough income and not too much in the way of savings or other capital. (p3)

[P]eople who are exempt from the test because of their condition ...[including when] you are pregnant and within either six weeks of giving birth or have given birth in the last two weeks and you are not entitled to maternity allowance or statutory maternity pay. (p16)

So, take a hypothetical woman who has a low household income, no savings and no recent employment history. She then becomes pregnant. The lack of recent employment means that she's not entitled to Maternity Allowance or Statutory Maternity Pay. If I have not missed out some crucial clause in your guide, then she is entitled to ESA, on the sole grounds of pregnancy - though for how long, I could not work out.

I am assuming, for the sake of clarity, that this pregnant woman does not have any other health-related issues and that the baby is in no danger should she work.

Is this correct? It sounds wrong, but I didn’t see where the “wrongness” is contradicted. OTOH I would have thought that if ESA were payable on those grounds, then "teenage mother on benefits" witch-hunters would be in full cry about ESA as well.